On the determining number of some graphs

Abstract

A subset S of vertices of a graph G is a determining set for G if every automorphism of G is uniquely determined by its action on S. The determining number of a graph G is the smallest integer r such that G has a determining set of size r. In this paper, we study the determining number of edge-corona product, hierarchical product of graphs and the determining number of blow-up of some graphs. Also, we investigate the determining number of the zero divisor graph of the ring [Formula: see text], for some values of n.

Keywords

• Determining set
• determining number
• edge-Corona product
• hierarchical product
• blow-up
• 05C15