On fixing sets of composition and corona product of graphs
Abstract
A fixing set J" of a graph G is a set of those vertices of the graph G which when assigned distinct labels removes all the automorphisms from the graph except the trivial one. The fixing number of a graph G, denoted by fix(G)} is the smallest cardinality of a fixing set of G. In this paper, we study the fixing number of composition product, G\ [Ga] and corona product, G\ QG2 of two graphs G\ and G2 with orders m and n respectively. We show that for a connected graph G\ and an arbitrary graph G2 having I > 1 components Gl2}Gl,...9Gl2imn- 1 > fix{G\[G2]) > m ( £ 1 For a connected graph G1 and an arbitrary graph G2} which are not asymmetric, we prove that fix(G\QG2) = mfix(G2). Further, for an arbitrary connected graph G1 and an arbitrary graph G2 we show that fix(G\ 0G2) = max{fix(G\)}mfix(G2)}. © 2018 Utilitas Mathematica Publishing Incorporated. All rights reserved.
