The Maximal Total Irregularity of Bicyclic Graphs

Abstract

In 2012, Abdo and Dimitrov defined the total irregularity of a graph $G=(V,E)$ as $\text{i}\text{r}{\text{r}}_t\left(G\right)=\left(1/2\right){\sum }_{u,v\in V}\left|d_G\left(u\right)-d_G\left(v\right)\right|$, where $d_G\left(u\right)$ denotes the vertex degree of a vertex $u\in V$. In this paper, we investigate the total irregularity of bicyclic graphs and characterize the graph with the maximal total irregularity among all bicyclic graphs on $n$ vertices.