INDEPENDENT DOMINATIONS IN DIRECT PRODUCT GRAPHS ARISING FROM EULER TOTIENT CAYLEY GRAPHS AND ARITHMETIC GRAPHS

Abstract

Graph Theory is one of the most flourishing branches of modern Mathematics finding widest applications in all most all branches of Science & Technology. It is applied in diverse areas such as social sciences, linguistics, physical sciences, communication engineering etc. Number Theory is one of the oldest branches of Mathematics, which inherited rich contributions from almost all greatest mathematicians, ancient and modern. Every branch of Mathematics employs some notion of a product that enables the combination or decomposition of its elemental structures. Product of graphs are introduced in graph theory very recently and developing rapidly. In this paper, we consider direct product graphs of Cayley graphs with Arithmetic graphs and present independent dominating set of these graphs.