Unique Response Roman Domination: Complexity and Algorithms
A function f : V ( G ) → { 0 , 1 , 2 } is called a Roman dominating function on G = ( V ( G ) , E ( G ) ) if for every vertex v with f ( v ) = 0 , there exists a vertex u ∈ N G ( v ) such that f ( u ) = 2 . A function f : V ( G ) → { 0 , 1 , 2 } induces an ordered partition ( V 0 , V 1 , V 2 ) of V...
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| Vydáno v: | Algorithmica Ročník 85; číslo 12; s. 3889 - 3927 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.12.2023
Springer Nature B.V |
| Témata: | |
| ISSN: | 0178-4617, 1432-0541 |
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| Abstract | A function
f
:
V
(
G
)
→
{
0
,
1
,
2
}
is called a
Roman dominating function
on
G
=
(
V
(
G
)
,
E
(
G
)
)
if for every vertex
v
with
f
(
v
)
=
0
, there exists a vertex
u
∈
N
G
(
v
)
such that
f
(
u
)
=
2
. A function
f
:
V
(
G
)
→
{
0
,
1
,
2
}
induces an ordered partition
(
V
0
,
V
1
,
V
2
)
of
V
(
G
), where
V
i
=
{
v
∈
V
(
G
)
:
f
(
v
)
=
i
}
for
i
∈
{
0
,
1
,
2
}
. A function
f
:
V
(
G
)
→
{
0
,
1
,
2
}
with ordered partition
(
V
0
,
V
1
,
V
2
)
is called a
unique response Roman function
if for every vertex
v
with
f
(
v
)
=
0
,
|
N
G
(
v
)
∩
V
2
|
≤
1
, and for every vertex
v
with
f
(
v
)
=
1
or 2,
|
N
G
(
v
)
∩
V
2
|
=
0
. A function
f
:
V
(
G
)
→
{
0
,
1
,
2
}
is called a
unique response Roman dominating function
(URRDF) on
G
if it is a unique response Roman function as well as a Roman dominating function on
G
. The weight of a unique response Roman dominating function
f
is the sum
f
(
V
(
G
)
)
=
∑
v
∈
V
(
G
)
f
(
v
)
, and the minimum weight of a unique response Roman dominating function on
G
is called the
unique response Roman domination number
of
G
and is denoted by
u
R
(
G
)
. Given a graph
G
, the
Min-URRDF
problem asks to find a unique response Roman dominating function of minimum weight on
G
. In this paper, we study the algorithmic aspects of
Min-URRDF
. We show that the decision version of
Min-URRDF
remains NP-complete for chordal graphs and bipartite graphs. We show that for a given graph with
n
vertices,
Min-URRDF
cannot be approximated within a ratio of
n
1
-
ε
for any
ε
>
0
unless
P
=
NP
. We also show that
Min-URRDF
can be approximated within a factor of
Δ
+
1
for graphs having maximum degree
Δ
. On the positive side, we design a linear-time algorithm to solve
Min-URRDF
for distance-hereditary graphs. Also, we show that
Min-URRDF
is polynomial-time solvable for interval graphs, and strengthen the result by showing that
Min-URRDF
can be solved in linear-time for proper interval graphs, a proper subfamily of interval graphs. |
|---|---|
| AbstractList | A function
f
:
V
(
G
)
→
{
0
,
1
,
2
}
is called a
Roman dominating function
on
G
=
(
V
(
G
)
,
E
(
G
)
)
if for every vertex
v
with
f
(
v
)
=
0
, there exists a vertex
u
∈
N
G
(
v
)
such that
f
(
u
)
=
2
. A function
f
:
V
(
G
)
→
{
0
,
1
,
2
}
induces an ordered partition
(
V
0
,
V
1
,
V
2
)
of
V
(
G
), where
V
i
=
{
v
∈
V
(
G
)
:
f
(
v
)
=
i
}
for
i
∈
{
0
,
1
,
2
}
. A function
f
:
V
(
G
)
→
{
0
,
1
,
2
}
with ordered partition
(
V
0
,
V
1
,
V
2
)
is called a
unique response Roman function
if for every vertex
v
with
f
(
v
)
=
0
,
|
N
G
(
v
)
∩
V
2
|
≤
1
, and for every vertex
v
with
f
(
v
)
=
1
or 2,
|
N
G
(
v
)
∩
V
2
|
=
0
. A function
f
:
V
(
G
)
→
{
0
,
1
,
2
}
is called a
unique response Roman dominating function
(URRDF) on
G
if it is a unique response Roman function as well as a Roman dominating function on
G
. The weight of a unique response Roman dominating function
f
is the sum
f
(
V
(
G
)
)
=
∑
v
∈
V
(
G
)
f
(
v
)
, and the minimum weight of a unique response Roman dominating function on
G
is called the
unique response Roman domination number
of
G
and is denoted by
u
R
(
G
)
. Given a graph
G
, the
Min-URRDF
problem asks to find a unique response Roman dominating function of minimum weight on
G
. In this paper, we study the algorithmic aspects of
Min-URRDF
. We show that the decision version of
Min-URRDF
remains NP-complete for chordal graphs and bipartite graphs. We show that for a given graph with
n
vertices,
Min-URRDF
cannot be approximated within a ratio of
n
1
-
ε
for any
ε
>
0
unless
P
=
NP
. We also show that
Min-URRDF
can be approximated within a factor of
Δ
+
1
for graphs having maximum degree
Δ
. On the positive side, we design a linear-time algorithm to solve
Min-URRDF
for distance-hereditary graphs. Also, we show that
Min-URRDF
is polynomial-time solvable for interval graphs, and strengthen the result by showing that
Min-URRDF
can be solved in linear-time for proper interval graphs, a proper subfamily of interval graphs. A function f:V(G)→{0,1,2} is called a Roman dominating function on G=(V(G),E(G)) if for every vertex v with f(v)=0, there exists a vertex u∈NG(v) such that f(u)=2. A function f:V(G)→{0,1,2} induces an ordered partition (V0,V1,V2) of V(G), where Vi={v∈V(G):f(v)=i} for i∈{0,1,2}. A function f:V(G)→{0,1,2} with ordered partition (V0,V1,V2) is called a unique response Roman function if for every vertex v with f(v)=0, |NG(v)∩V2|≤1, and for every vertex v with f(v)=1 or 2, |NG(v)∩V2|=0. A function f:V(G)→{0,1,2} is called a unique response Roman dominating function (URRDF) on G if it is a unique response Roman function as well as a Roman dominating function on G. The weight of a unique response Roman dominating function f is the sum f(V(G))=∑v∈V(G)f(v), and the minimum weight of a unique response Roman dominating function on G is called the unique response Roman domination number of G and is denoted by uR(G). Given a graph G, the Min-URRDF problem asks to find a unique response Roman dominating function of minimum weight on G. In this paper, we study the algorithmic aspects of Min-URRDF. We show that the decision version of Min-URRDF remains NP-complete for chordal graphs and bipartite graphs. We show that for a given graph with n vertices, Min-URRDF cannot be approximated within a ratio of n1-ε for any ε>0 unless P=NP. We also show that Min-URRDF can be approximated within a factor of Δ+1 for graphs having maximum degree Δ. On the positive side, we design a linear-time algorithm to solve Min-URRDF for distance-hereditary graphs. Also, we show that Min-URRDF is polynomial-time solvable for interval graphs, and strengthen the result by showing that Min-URRDF can be solved in linear-time for proper interval graphs, a proper subfamily of interval graphs. |
| Author | Chaudhary, Juhi Banerjee, Sumanta Pradhan, Dinabandhu |
| Author_xml | – sequence: 1 givenname: Sumanta surname: Banerjee fullname: Banerjee, Sumanta organization: Department of Mathematics and Computing, Indian Institute of Technology (ISM) – sequence: 2 givenname: Juhi surname: Chaudhary fullname: Chaudhary, Juhi organization: Department of Computer Science, Ben-Gurion University of the Negev – sequence: 3 givenname: Dinabandhu surname: Pradhan fullname: Pradhan, Dinabandhu email: dina@iitism.ac.in organization: Department of Mathematics and Computing, Indian Institute of Technology (ISM) |
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| Cites_doi | 10.1016/j.dam.2016.09.035 10.1007/s10878-012-9500-0 10.1016/0020-0190(84)90126-1 10.1016/j.dam.2016.03.017 10.1007/s00453-020-00705-7 10.1016/j.tcs.2019.08.017 10.1145/2591796.2591884 10.1016/j.dam.2021.08.020 10.1080/00029890.2000.12005243 10.1287/moor.4.3.233 10.1016/j.disc.2003.06.004 10.1016/j.dam.2019.01.038 10.1007/3-540-63890-3_37 10.1007/s12190-020-01345-4 10.1137/1.9780898719796 10.1016/j.dam.2022.09.017 10.1016/0020-0190(88)90091-9 10.1038/scientificamerican1299-136 10.1016/0196-6774(85)90001-X 10.1080/00207160.2017.1301437 10.1007/978-3-642-58412-1 10.1145/800157.805047 10.1002/net.1 10.1016/j.dam.2008.01.011 10.1016/j.ipl.2018.01.004 10.1016/j.disc.2007.03.020 10.7151/dmgt.2067 10.1016/j.dam.2011.03.013 10.1016/j.tcs.2022.02.006 10.1137/S0097539792238431 10.1016/S0166-218X(98)00060-2 10.1016/0166-218X(90)90131-U 10.1016/j.dam.2017.10.027 10.1016/S0020-0190(03)00298-9 10.1016/S0166-218X(97)00125-X 10.1137/0217032 10.1016/j.dam.2005.07.011 10.1016/j.dam.2015.11.013 10.1016/0304-3975(87)90067-3 10.1016/j.akcej.2020.01.005 10.1007/s10878-019-00457-3 10.1016/0095-8956(86)90043-2 |
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| Issue | 12 |
| Keywords | Domination Roman domination Polynomial-time algorithm Unique response Roman domination Unique response Roman function NP-completeness |
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| References | Liedloff, Kloks, Liu, Peng (CR35) 2008; 156 Bertossi (CR10) 1984; 19 Chang (CR13) 1998; 6 Chen, Lu (CR17) 2019; 39 Henning, Klostermeyer (CR29) 2017; 217 Lee, Chang (CR34) 2006; 154 D’Atri, Moscarini (CR21) 1988; 17 Ausiello, Protasi, Spaccamela, Gambosi, Crescenzi, Kann (CR4) 1999 Chellali, Haynes, Hedetniemi, McRae (CR16) 2016; 204 CR33 CR32 Falk, Thomas (CR23) 2001; 37 Hammer, Maffray (CR27) 1990; 27 Banerjee, Keil, Pradhan (CR8) 2019; 796 Banerjee, Henning, Pradhan (CR7) 2021; 391 Zhang, Li, Jiang, Shao (CR51) 2018; 134 Garey, Johnson (CR25) 1990 Ahangar, Chellali, Samodivkin (CR1) 2017; 94 Poureidi (CR40) 2022; 911 Yeh, Chang (CR49) 1998; 87 Panda, Das (CR39) 2003; 87 Brandstädt, Chepoi, Dargan (CR11) 1998; 82 Ahangar, Henning, Löwenstein, Zhao, Samodivkin (CR3) 2014; 27 CR45 Bandelt, Mulder (CR5) 1986; 41 Beeler, Haynes, Hedetniemi (CR9) 2016; 211 Pradhan, Banerjee, Liu (CR41) 2022; 319 Yue, Wei, Li, Liu (CR50) 2018; 338 Padamutham, Palagiri (CR37) 2020; 64 Haiko, Brandstädt (CR26) 1987; 53 ReVelle, Rosing (CR44) 2000; 107 Banerjee, Henning, Pradhan (CR6) 2020; 39 Padamutham, Palagiri (CR38) 2020; 17 CR15 CR14 CR12 Ahangar, Chellali, Sheikholeslami (CR2) 2020; 364 Targhi, Rad, Volkmann (CR48) 2011; 159 Chvatal (CR18) 1979; 4 Cockayne, Dreyer, Hedetniemi, Hedetniemi (CR19) 2004; 278 Rubalcaba, Slater (CR46) 2007; 307 Zhao, Li, Zhao, Zhang (CR52) 2018; 105 Haynes, Henning (CR28) 2019; 260 Rad, Liu (CR42) 2012; 54 CR22 Lin, Ku, Hsu (CR36) 2020; 82 Hsieh, Ho, Hsu, Ko, Chen (CR31) 2002; 15 CR20 Ramalingam, Rangan (CR43) 1988; 27 Stewart (CR47) 1999; 281 Farber, Keil (CR24) 1985; 6 Henning, Klostermeyer, MacGillivray (CR30) 2018; 236 S Banerjee (1171_CR6) 2020; 39 MR Garey (1171_CR25) 1990 EE Targhi (1171_CR48) 2011; 159 MA Henning (1171_CR29) 2017; 217 RR Rubalcaba (1171_CR46) 2007; 307 BS Panda (1171_CR39) 2003; 87 CS ReVelle (1171_CR44) 2000; 107 1171_CR32 1171_CR33 C Padamutham (1171_CR38) 2020; 17 HA Ahangar (1171_CR1) 2017; 94 MS Chang (1171_CR13) 1998; 6 V Chvatal (1171_CR18) 1979; 4 HA Ahangar (1171_CR3) 2014; 27 CC Lin (1171_CR36) 2020; 82 G Ramalingam (1171_CR43) 1988; 27 1171_CR20 M Haiko (1171_CR26) 1987; 53 M Liedloff (1171_CR35) 2008; 156 1171_CR22 PL Hammer (1171_CR27) 1990; 27 CM Lee (1171_CR34) 2006; 154 A Poureidi (1171_CR40) 2022; 911 A D’Atri (1171_CR21) 1988; 17 SY Hsieh (1171_CR31) 2002; 15 HG Yeh (1171_CR49) 1998; 87 I Stewart (1171_CR47) 1999; 281 H Chen (1171_CR17) 2019; 39 1171_CR12 J Yue (1171_CR50) 2018; 338 1171_CR14 N Falk (1171_CR23) 2001; 37 C Padamutham (1171_CR37) 2020; 64 1171_CR15 N Zhao (1171_CR52) 2018; 105 M Chellali (1171_CR16) 2016; 204 TW Haynes (1171_CR28) 2019; 260 NJ Rad (1171_CR42) 2012; 54 HA Ahangar (1171_CR2) 2020; 364 S Banerjee (1171_CR7) 2021; 391 X Zhang (1171_CR51) 2018; 134 RA Beeler (1171_CR9) 2016; 211 AA Bertossi (1171_CR10) 1984; 19 G Ausiello (1171_CR4) 1999 M Farber (1171_CR24) 1985; 6 S Banerjee (1171_CR8) 2019; 796 D Pradhan (1171_CR41) 2022; 319 EJ Cockayne (1171_CR19) 2004; 278 MA Henning (1171_CR30) 2018; 236 1171_CR45 A Brandstädt (1171_CR11) 1998; 82 HJ Bandelt (1171_CR5) 1986; 41 |
| References_xml | – ident: CR45 – volume: 41 start-page: 182 year: 1986 end-page: 208 ident: CR5 article-title: Distance-hereditary graphs publication-title: J. Combin. Theory Ser. B – ident: CR22 – volume: 236 start-page: 235 year: 2018 end-page: 245 ident: CR30 article-title: Perfect Roman domination in trees publication-title: Discrete Appl. Math. – volume: 911 start-page: 70 year: 2022 end-page: 79 ident: CR40 article-title: Algorithm and hardness results in double Roman domination of graphs publication-title: Theor. Comput. Sci. – volume: 391 year: 2021 ident: CR7 article-title: Perfect Italian domination in cographs publication-title: Appl. Math. Comput. – ident: CR12 – volume: 37 start-page: 117 year: 2001 end-page: 128 ident: CR23 article-title: Homogeneous sets and domination: a linear time algorithm for distance-hereditary graphs publication-title: Networks – volume: 211 start-page: 23 year: 2016 end-page: 29 ident: CR9 article-title: Double Roman domination publication-title: Discrete Appl. Math. – volume: 204 start-page: 22 year: 2016 end-page: 28 ident: CR16 article-title: Roman -domination publication-title: Discrete Appl. Math. – volume: 87 start-page: 245 year: 1998 end-page: 253 ident: CR49 article-title: Weighted connected domination and Steiner trees in distance-hereditary graphs publication-title: Discrete Appl. Math. – volume: 217 start-page: 557 year: 2017 end-page: 564 ident: CR29 article-title: Italian domination in trees publication-title: Discrete Appl. Math. – volume: 307 start-page: 3194 year: 2007 end-page: 3200 ident: CR46 article-title: Roman dominating influence parameters publication-title: Discrete Math. – volume: 338 start-page: 669 year: 2018 end-page: 675 ident: CR50 article-title: On the double Roman domination of graphs publication-title: Appl. Math. Comput. – volume: 17 start-page: 521 year: 1988 end-page: 538 ident: CR21 article-title: Distance-hereditary graphs, steiner trees, and connected domination publication-title: SIAM J. Comput. – ident: CR15 – volume: 39 start-page: 90 year: 2020 end-page: 114 ident: CR6 article-title: Algorithmic results on double Roman domination in graphs publication-title: J. Comb. Optim. – volume: 27 start-page: 85 year: 1990 end-page: 99 ident: CR27 article-title: Completely separable graphs publication-title: Discrete Appl. Math. – volume: 39 start-page: 13 year: 2019 end-page: 21 ident: CR17 article-title: A Note on Roman -domination problem in graphs publication-title: Discuss. Math. Graph Theory – volume: 64 start-page: 89 year: 2020 end-page: 102 ident: CR37 article-title: Algorithmic aspects of Roman domination in graphs publication-title: J. Appl. Math. Comput. – volume: 54 start-page: 133 year: 2012 end-page: 140 ident: CR42 article-title: Trees with strong equality between the Roman domination number and the unique response Roman domination number publication-title: Australas. J. Comb. – ident: CR32 – volume: 17 start-page: 1081 year: 2020 end-page: 1086 ident: CR38 article-title: Complexity of Roman -domination and the double Roman domination in graphs publication-title: AKCE Int. J. Graphs Comb. – volume: 319 start-page: 271 year: 2022 end-page: 295 ident: CR41 article-title: Perfect Italian domination in graphs: Complexity and algorithms publication-title: Discrete Appl. Math. – year: 1999 ident: CR4 publication-title: Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties – year: 1990 ident: CR25 publication-title: Computers and Intractability, A Guide to the Theory of NP-Completeness – volume: 260 start-page: 164 year: 2019 end-page: 177 ident: CR28 article-title: Perfect Italian domination in trees publication-title: Discrete Appl. Math. – volume: 159 start-page: 1110 year: 2011 end-page: 1117 ident: CR48 article-title: Unique response Roman domination in graphs publication-title: Discrete Appl. Math. – volume: 15 start-page: 488 year: 2002 end-page: 518 ident: CR31 article-title: Characterization of efficiently parallel solvable problems on distance-hereditary graphs publication-title: Discrete Math. – volume: 105 start-page: 165 year: 2018 end-page: 183 ident: CR52 article-title: The unique response Roman domination in trees publication-title: J. Combin. Math. Combin. Comput. – volume: 156 start-page: 3400 year: 2008 end-page: 3415 ident: CR35 article-title: Efficient algorithms for Roman domination on some classes of graphs publication-title: Discrete Appl. Math. – volume: 87 start-page: 153 year: 2003 end-page: 161 ident: CR39 article-title: A linear time recognition algorithm for proper interval graphs publication-title: Inf. Process. Lett. – ident: CR14 – volume: 796 start-page: 1 year: 2019 end-page: 21 ident: CR8 article-title: Perfect Roman domination in graphs publication-title: Theor. Comput. Sci. – volume: 53 start-page: 257 year: 1987 end-page: 265 ident: CR26 article-title: The NP-completeness of Steiner tree and dominating set for chordal bipartite graphs publication-title: Theor. Comput. Sci. – ident: CR33 – volume: 19 start-page: 37 year: 1984 end-page: 40 ident: CR10 article-title: Dominating sets for split and bipartite graphs publication-title: Inf. Process. Lett. – volume: 281 start-page: 136 year: 1999 end-page: 138 ident: CR47 article-title: Defend the Roman empire! publication-title: Sci. Am. – volume: 278 start-page: 11 year: 2004 end-page: 22 ident: CR19 article-title: Roman domination in graphs publication-title: Discrete Math. – volume: 134 start-page: 31 year: 2018 end-page: 34 ident: CR51 article-title: Double Roman domination in trees publication-title: Inf. Process. Lett. – volume: 82 start-page: 43 year: 1998 end-page: 77 ident: CR11 article-title: The algorithmic use of hypertree structure and maximum neighborhood orderings publication-title: Discrete Appl. Math. – volume: 4 start-page: 233 year: 1979 end-page: 235 ident: CR18 article-title: A greedy heuristic for the set-covering problem publication-title: Math. Oper. Res. – volume: 364 year: 2020 ident: CR2 article-title: Outer independent double Roman domination publication-title: Appl. Math. Comput. – volume: 154 start-page: 525 year: 2006 end-page: 536 ident: CR34 article-title: Distance-hereditary graphs are clique-perfect publication-title: Discrete Appl. Math. – volume: 6 start-page: 1671 year: 1998 end-page: 1694 ident: CR13 article-title: Efficient algorithms for the domination problems on interval and circular-arc graphs publication-title: SIAM J. Comput. – volume: 6 start-page: 309 year: 1985 end-page: 321 ident: CR24 article-title: Domination in permutation graphs publication-title: J. Algorithms – volume: 82 start-page: 2809 year: 2020 end-page: 2840 ident: CR36 article-title: Paired-Domination Problem on Distance-Hereditary Graphs publication-title: Algorithmica – volume: 94 start-page: 2547 year: 2017 end-page: 2557 ident: CR1 article-title: Outer independent Roman dominating functions in graphs publication-title: Int. J. Comput. Math. – volume: 27 start-page: 271 year: 1988 end-page: 274 ident: CR43 article-title: A unified approach to domination problems on interval graphs publication-title: Inf. Process. Lett. – volume: 27 start-page: 241 year: 2014 end-page: 255 ident: CR3 article-title: Signed Roman domination in graphs publication-title: J. Comb. Optim. – volume: 107 start-page: 585 year: 2000 end-page: 594 ident: CR44 article-title: Defendens imperium romanum: a classical problem in military strategy publication-title: Am. Math. Monthly – ident: CR20 – volume: 217 start-page: 557 year: 2017 ident: 1171_CR29 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2016.09.035 – volume: 27 start-page: 241 year: 2014 ident: 1171_CR3 publication-title: J. Comb. Optim. doi: 10.1007/s10878-012-9500-0 – volume: 19 start-page: 37 year: 1984 ident: 1171_CR10 publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(84)90126-1 – volume: 211 start-page: 23 year: 2016 ident: 1171_CR9 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2016.03.017 – ident: 1171_CR33 – volume: 82 start-page: 2809 year: 2020 ident: 1171_CR36 publication-title: Algorithmica doi: 10.1007/s00453-020-00705-7 – volume: 796 start-page: 1 year: 2019 ident: 1171_CR8 publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2019.08.017 – ident: 1171_CR22 doi: 10.1145/2591796.2591884 – volume: 319 start-page: 271 year: 2022 ident: 1171_CR41 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2021.08.020 – volume: 107 start-page: 585 year: 2000 ident: 1171_CR44 publication-title: Am. Math. Monthly doi: 10.1080/00029890.2000.12005243 – volume: 338 start-page: 669 year: 2018 ident: 1171_CR50 publication-title: Appl. Math. Comput. – volume: 4 start-page: 233 year: 1979 ident: 1171_CR18 publication-title: Math. Oper. Res. doi: 10.1287/moor.4.3.233 – volume: 278 start-page: 11 year: 2004 ident: 1171_CR19 publication-title: Discrete Math. doi: 10.1016/j.disc.2003.06.004 – volume: 54 start-page: 133 year: 2012 ident: 1171_CR42 publication-title: Australas. J. Comb. – volume: 260 start-page: 164 year: 2019 ident: 1171_CR28 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2019.01.038 – ident: 1171_CR14 doi: 10.1007/3-540-63890-3_37 – ident: 1171_CR32 – volume: 64 start-page: 89 year: 2020 ident: 1171_CR37 publication-title: J. Appl. Math. Comput. doi: 10.1007/s12190-020-01345-4 – ident: 1171_CR12 doi: 10.1137/1.9780898719796 – ident: 1171_CR15 doi: 10.1016/j.dam.2022.09.017 – volume: 27 start-page: 271 year: 1988 ident: 1171_CR43 publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(88)90091-9 – volume: 281 start-page: 136 year: 1999 ident: 1171_CR47 publication-title: Sci. Am. doi: 10.1038/scientificamerican1299-136 – volume: 6 start-page: 309 year: 1985 ident: 1171_CR24 publication-title: J. Algorithms doi: 10.1016/0196-6774(85)90001-X – volume: 94 start-page: 2547 year: 2017 ident: 1171_CR1 publication-title: Int. J. Comput. Math. doi: 10.1080/00207160.2017.1301437 – volume-title: Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties year: 1999 ident: 1171_CR4 doi: 10.1007/978-3-642-58412-1 – ident: 1171_CR20 doi: 10.1145/800157.805047 – volume: 15 start-page: 488 year: 2002 ident: 1171_CR31 publication-title: Discrete Math. – volume: 37 start-page: 117 year: 2001 ident: 1171_CR23 publication-title: Networks doi: 10.1002/net.1 – volume: 156 start-page: 3400 year: 2008 ident: 1171_CR35 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2008.01.011 – volume: 134 start-page: 31 year: 2018 ident: 1171_CR51 publication-title: Inf. Process. Lett. doi: 10.1016/j.ipl.2018.01.004 – volume: 307 start-page: 3194 year: 2007 ident: 1171_CR46 publication-title: Discrete Math. doi: 10.1016/j.disc.2007.03.020 – volume: 364 year: 2020 ident: 1171_CR2 publication-title: Appl. Math. Comput. – volume: 39 start-page: 13 year: 2019 ident: 1171_CR17 publication-title: Discuss. Math. Graph Theory doi: 10.7151/dmgt.2067 – volume: 159 start-page: 1110 year: 2011 ident: 1171_CR48 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2011.03.013 – volume: 911 start-page: 70 year: 2022 ident: 1171_CR40 publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2022.02.006 – volume: 6 start-page: 1671 year: 1998 ident: 1171_CR13 publication-title: SIAM J. Comput. doi: 10.1137/S0097539792238431 – volume: 105 start-page: 165 year: 2018 ident: 1171_CR52 publication-title: J. Combin. Math. Combin. Comput. – volume-title: Computers and Intractability, A Guide to the Theory of NP-Completeness year: 1990 ident: 1171_CR25 – volume: 87 start-page: 245 year: 1998 ident: 1171_CR49 publication-title: Discrete Appl. Math. doi: 10.1016/S0166-218X(98)00060-2 – volume: 27 start-page: 85 year: 1990 ident: 1171_CR27 publication-title: Discrete Appl. Math. doi: 10.1016/0166-218X(90)90131-U – volume: 236 start-page: 235 year: 2018 ident: 1171_CR30 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2017.10.027 – volume: 87 start-page: 153 year: 2003 ident: 1171_CR39 publication-title: Inf. Process. Lett. doi: 10.1016/S0020-0190(03)00298-9 – ident: 1171_CR45 – volume: 82 start-page: 43 year: 1998 ident: 1171_CR11 publication-title: Discrete Appl. Math. doi: 10.1016/S0166-218X(97)00125-X – volume: 17 start-page: 521 year: 1988 ident: 1171_CR21 publication-title: SIAM J. Comput. doi: 10.1137/0217032 – volume: 154 start-page: 525 year: 2006 ident: 1171_CR34 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2005.07.011 – volume: 204 start-page: 22 year: 2016 ident: 1171_CR16 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2015.11.013 – volume: 53 start-page: 257 year: 1987 ident: 1171_CR26 publication-title: Theor. Comput. Sci. doi: 10.1016/0304-3975(87)90067-3 – volume: 17 start-page: 1081 year: 2020 ident: 1171_CR38 publication-title: AKCE Int. J. Graphs Comb. doi: 10.1016/j.akcej.2020.01.005 – volume: 39 start-page: 90 year: 2020 ident: 1171_CR6 publication-title: J. Comb. Optim. doi: 10.1007/s10878-019-00457-3 – volume: 391 year: 2021 ident: 1171_CR7 publication-title: Appl. Math. Comput. – volume: 41 start-page: 182 year: 1986 ident: 1171_CR5 publication-title: J. Combin. Theory Ser. B doi: 10.1016/0095-8956(86)90043-2 |
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| Snippet | A function
f
:
V
(
G
)
→
{
0
,
1
,
2
}
is called a
Roman dominating function
on
G
=
(
V
(
G
)
,
E
(
G
)
)
if for every vertex
v
with
f
(
v
)
=
0
, there exists... A function f:V(G)→{0,1,2} is called a Roman dominating function on G=(V(G),E(G)) if for every vertex v with f(v)=0, there exists a vertex u∈NG(v) such that... |
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| SubjectTerms | Algorithm Analysis and Problem Complexity Algorithms Apexes Approximation Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Graph theory Graphs Mathematical functions Mathematics of Computing Minimum weight Polynomials Theory of Computation |
| Title | Unique Response Roman Domination: Complexity and Algorithms |
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