Some Results on Gamma Graphs

Authors

  • Krupali Bhatt

Keywords:

Gamma sets, Gamma graphs, Cartesian Product, Join, Corona of two graphs

Abstract

In a graph   the set of vertices  is a dominating set if every vertex in  is adjacent to at least one vertex in . The domination number  of G equals the minimum cardinality of a dominating set S in  and the set  is known as -set. The gamma graph of a graph G has its γ-sets as vertices and any two vertices are adjacent if the corresponding γ-sets differ exactly by one vertex. In this paper we try to include the study on the gamma graphs on corona, join and cartesian product cycles and paths.

Downloads

Download data is not yet available.

References

K. Subramanian and N. Sridharan, γ-graph of a graph, Bull. Kerala Math. Assoc., 5(1) (2008), 17-34.

N. Sridharan and K. Subramanian, Trees and unicyclic graphs are γ-graphs, J. Combin. Math. Combin. Comput., 69 (2009), 231-236.

S. A. Lakshmanan, A. Vijayakumar, The gamma graph of a graph, AKCE International Journal of Graphs and Combinatorics 7 (2010), 53–59.

R. Balakrishnan and K. Ranganathan, A textbook of graph theory, Springer (1999).

G. H. Fricke, S. M. Hedetniemi, S. T. Hedetniemi, K. R. Hutson, γ−graphs of graphs, Discuss. Math. Graph Theory 31 (2011), 517-531.

R. Isaac and K. Bhatt, A study on the gamma graph of cycle C_(3k+1), Journal of Computational Mathematica, 7(2) (2023), 102-106.

Anna Bien, Gamma graphs of some special classes of trees. Annales Mathematicae Silesianae 29 (2015), 25–34.

Christopher M. Bommel, A bipartite graph that is not the γ-graph of a bipartite graph, Available at arXiv:2011.01763v1[math.CO], 3 Nov 2020.

C.M. Mynhardt and L. Teshima, A note on some variations of the γ−graph. J. Combin. Math. Combin. Comput., 104:217–230, 2018.

Carmelito E. Go and Sergio R. Canoy, Domination in the corona and join of graphs, International Mathematical Forum, 6(16) (2011), 763-771.

E. Connelly, S.T. Hedetniemi and K.R. Hutson, A Note on γ−Graphs, AKCE International Journal of Graphs and Combinatorics 8 (2011), 23–31.

N. Sridharan, S. Amutha, S. B. Rao, Induced Subgraph of Gamma Graphs, World Scientific, Discrete Mathematics, Algorithms and Applications, Vol. 5, No. 3(2013).

T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of domination in graphs, Marcel Dekker, Inc. (1998).

V.Anusuya, R. Kala, Modified γ graph-G(γm) of some grid graphs, Palestine Journal of Mathematics, 9(2) (2020), 691-697.

Additional Files

Published

10-08-2024

How to Cite

Krupali Bhatt. (2024). Some Results on Gamma Graphs. Vidhyayana - An International Multidisciplinary Peer-Reviewed E-Journal - ISSN 2454-8596, 10(1). Retrieved from http://j.vidhyayanaejournal.org/index.php/journal/article/view/1928