On the Variance-Type Graph Irregularity Measures

Abstract

Bell's degree-variance Var$\!{}_{B}$ for a graph $G$, with the degree sequence ($d_1,d_2,\ldots,d_n$) and size $m$, is defined as $Var\!_{B} (G)=\frac{1}{n} \sum _{i=1}^{n}\left[d_{i} -\frac{2m}{n}\right]^{2}$. In this paper, a new version of the irregularity measures of variance-type, denoted by $Var_q$, is introduced and discussed. Based on a comparative study, it is demonstrated that the newly proposed irregularity measure $Var_q$ possess a better discrimination ability than the classical Bell's degree-variance in several cases.

Keywords

• non-regular graphs
• irregularity measures
• degree variance