Characterization of certain families of modular multiplicative divisor graphs
A modular multiplicative divisor (MMD) labelling of a graph G with p vertices and q edges is a bijection f from the set of all vertices to the set of positive integers {1, 2,…,p} such that the sum of all edge labels f*(uv)=f(u)f(v)(modp); uv∈E(G) is a multiple of p. In this paper, we characterize ce...
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| Vydané v: | Journal of Taibah University for Science Ročník 11; číslo 2; s. 294 - 297 |
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Elsevier B.V
01.03.2017
Taylor & Francis Group |
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| Abstract | A modular multiplicative divisor (MMD) labelling of a graph G with p vertices and q edges is a bijection f from the set of all vertices to the set of positive integers {1, 2,…,p} such that the sum of all edge labels f*(uv)=f(u)f(v)(modp); uv∈E(G) is a multiple of p. In this paper, we characterize certain classes of MMD graphs. This result is a solution to the open problem posed by G. Sethuraman in AKCE International Journal of Graphs and Combinatorics, No. 1 (2009) 229–236. In addition, we discuss the role of MMD labelling in obtaining cyclic decompositions of certain families of graphs into specific graphs. |
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| AbstractList | A modular multiplicative divisor (MMD) labelling of a graph G with p vertices and q edges is a bijection f from the set of all vertices to the set of positive integers {1, 2, …, p} such that the sum of all edge labels f*(uv) = f(u)f(v)(modp); uv ∈ E(G) is a multiple of p. In this paper, we characterize certain classes of MMD graphs. This result is a solution to the open problem posed by G. Sethuraman in AKCE International Journal of Graphs and Combinatorics, No. 1 (2009) 229–236. In addition, we discuss the role of MMD labelling in obtaining cyclic decompositions of certain families of graphs into specific graphs. A modular multiplicative divisor (MMD) labelling of a graph G with p vertices and q edges is a bijection f from the set of all vertices to the set of positive integers {1, 2,…,p} such that the sum of all edge labels f*(uv)=f(u)f(v)(modp); uv∈E(G) is a multiple of p. In this paper, we characterize certain classes of MMD graphs. This result is a solution to the open problem posed by G. Sethuraman in AKCE International Journal of Graphs and Combinatorics, No. 1 (2009) 229–236. In addition, we discuss the role of MMD labelling in obtaining cyclic decompositions of certain families of graphs into specific graphs. |
| Author | Revathi, R. Ganesh, S. |
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| Cites_doi | 10.17485/ijst/2014/v7i12.25 10.1016/S0012-365X(02)00455-7 |
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| References | Harary (bib0055) 1972 Gallian (bib0060) 2007; 14 Revathi, Rajeswari (bib0065) 2014; 7 Revathi, Rajeswari (bib0070) 2013 Arumugam, Bloom, Miller, Ryan (bib0080) 2009; 1 Sethuraman, Selvaraju (bib0085) 2001; 32 Kathiresan, Amutha (bib0095) 2004; 35 Sethuraman, Selvaraju (bib0090) 2001; 32 Revathi, Rajeswari (bib0075) 2014; 89 Sethuraman, Selvaraju (bib0100) 2003; 260 bib0055 Revathi R. (bib0065) 2014; 7 Kathiresan K.M. (bib0095) 2004; 35 Sethuraman G. (bib0100) 2003; 260 Gallian J.A. (bib0060) 2007; 14 Sethuraman G. (bib0090) 2001; 32 Arumugam S. (bib0080) 2009; 1 Revathi R. (bib0070) 2013 Sethuraman G. (bib0085) 2001; 32 Revathi R. (bib0075) 2014; 89 |
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| Title | Characterization of certain families of modular multiplicative divisor graphs |
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