The Lowest Total Irregularity of a Completely Segregated ?-Bicyclic Graph

Abstract

A simple linked graph with exactly the same number of edges as vertices plus one is called a bicyclic graph. A completely segregated bicyclic network is one in which any two neighboring vertices have different degrees. Total Irregularity of a graph is defined as: irr_t(G)= . In this paper, total irregularity of totally segregated - bicyclic graph is discussed and some properties of totally segregated - bicyclic graph G with =4 and n₄(G)=1 is found. The basic bicycle denoted by (p,q,1) is obtained from two vertex-disjoint cycles Cp and Cq by identifying one vertex of Cp and one vertex of Cq.