Edge Domination in Euler Totient Cayley Graph

K.J. Sangeetha, B. Maheswari

Abstract: Graph Theory has been realized as one of the most flourishing branches of modern Mathematics finding widest applications in all most all branches of Sciences, Social Sciences, Engineering, Computer Science, etc. Number Theory is one of the oldest branches of Mathematics, which inherited rich contributions from almost all greatest mathematicians, ancient and modern. Nathanson [1] paved the way for the emergence of a new class of graphs, namely Arithmetic Graphs by introducing the concepts of Number Theory. Using the number theoretic function, the Euler totient function, we have defined an Euler totient Cayley graph and in this paper we study the Edge domination in Euler totient Cayley graph. This paper is devoted for the study of minimum edge cover, edge covering number, minimal edge dominating set and edge domination number of Euler totient Cayley graph in two cases when n is even and when n is odd.

Keywords: Euler Totient Cayley Graph, Edge cover, Minimum edge cover, Edge covering number, Edge domination, Minimal edge domination, Edge domination number