On the Variance-Type Graph Irregularity Measures

Bell's degree-variance Var$!{}_{B}$ for a graph $G$, with the degree sequence ($d_1,d_2,cdots,d_n$) 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.