On the algebraic connectivity of some token graphs
The k -token graph F k ( G ) of a graph G is the graph whose vertices are the k -subsets of vertices from G , two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G . It was proved that the algebraic connectivity of F k ( G ) equals the algebraic connectivi...
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| Vydáno v: | Journal of algebraic combinatorics Ročník 60; číslo 1; s. 45 - 56 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.08.2024
Springer Nature B.V |
| Témata: | |
| ISSN: | 0925-9899, 1572-9192 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | The
k
-token graph
F
k
(
G
)
of a graph
G
is the graph whose vertices are the
k
-subsets of vertices from
G
, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in
G
. It was proved that the algebraic connectivity of
F
k
(
G
)
equals the algebraic connectivity of
G
with a proof using random walks and interchange of processes on a weighted graph. However, no algebraic or combinatorial proof is known, and it would be a hit in the area. In this paper, we algebraically prove that the algebraic connectivity of
F
k
(
G
)
equals the one of
G
for new infinite families of graphs, such as trees, some graphs with hanging trees, and graphs with minimum degree large enough. Some examples of these families are the following: the cocktail party graph, the complement graph of a cycle, and the complete multipartite graph. |
|---|---|
| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0925-9899 1572-9192 |
| DOI: | 10.1007/s10801-024-01323-0 |