Some Properties of Direct Product Graphs of Cayley Graphs with Arithmetic Graphs

Abstract

Nathanson was the pioneer in introducing the concepts of Number Theory, particularly, the “Theory of Congruences” in Graph Theory, thus paving way for the emergence of a new class of graphs, namely “Arithmetic Graphs”. Cayley graphs are another class of graphs associated with the elements of a group. If this group is associated with some arithmetic function then the Cayley graph becomes an Arithmetic graph. In this paper, we present some results related to basic properties of direct product graphs of Euler totient Cayley graphs with Arithmetic graph.