Total Irregularity of Indu-Bala Product of Graphs

Abstract

The total irregularity of a simple undirected graph G is defined as       ,   1 2 t G G u v V G irr G d u d v     , where   G d u denotes the degree of a vertex u V G    . The Indu-Bala product of G1 and G2 is denoted by G G 1 2  and is obtained from two disjoint copies of the join G G 1 2  of G1 and G2 by joining the corresponding vertices in the two copies of G2 . In this paper, the total irregularity of G G 1 2  is obtained in terms of the total irregularities of G1 and G2 .