Cayley Graphs Versus Algebraic Graphs

Pranjali Pranjali, Amit Kumar, Tanuja Yadav

Abstract


Let Γ be a finite group and let S ⊆ Γ be a subset. The Cayley graph, denoted byCay(Γ, S) has vertex set Γ and two distinct vertices x, y ∈ Γ are joined by a directed edge fromx to y if and only if there exists s ∈ S such that x = sy. In this manuscript, we characterize the generating setsS for which Cay(Γ, S) is isomorphic to somealgebraic graphs, namely, unit graphs, co-unit graphs, total graph and co-total graphs.

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References


Beny, G. A. and Rakhmonov, Z., Number of Cayley graph of finite group Zn that is undirected, Proceedings of third Conference and Workshop on Group theory, University of Tehran, 9-10 March (2011), 8-11.

Cayley, A., Desiderata and suggestions; The Theory of groups: graphical representation, American Journal of Mathematics, 1(2 (1878), 174–176.

Harary, F., Graph Theory, Addison-Wesley Publ. Comp. Reading. MA, 1969.

Jacobson, N., Lectures in Abstract Algebra, East-West Press P. Ltd., New Delhi, 1951.

Maimani, H. R., Pournaki, M. R., Tehranian, A. and Yassemi, S. Graphs Attached to Rings

Revisited, Arabian Journal for Science and Engineering (2011), 36:997




DOI: https://doi.org/10.22342/jims.27.2.800.130-136

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