Let G = (V,E), V = {1,2, . . . ,n}, be a simple graph without isolated vertices, with vertex degree sequence d1 ≥ d2 ≥ ·· · ≥ dn > 0, di = d(i). A graph G is regular if and only if d1 = d2 = · · · = dn. A graph invariant I(G) is measure of irregularity of graph G with the property I(G) = 0 if and only ifG is regular, and I(G)> 0 otherwise. In this paper we introduce some new 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 n...

In this paper, we tighten the concise Turán theorem for irregular graphs, using spectral and non-spectral proofs. We then investigate to what extent Turán’s theorem can be similarly strengthened for generalized r-partite graphs.

Measures of the irregularity of chemical graphs could be helpful for QSAR/QSPR studies and for the descriptive purposes of biological and chemical properties, such as melting and boiling points, toxicity and resistance. Here we consider the following four established irregularity measures: the irregularity index by Albertson, the total irregularity, the variance of vertex degrees and the Collat...

Despite abundant research on the distribution of glottal stops and glottalization in English and other languages, it is still unclear which factors matter most in predicting where glottal stops occur. In this study, logistic mixed-effects regression modeling is used to predict the occurrence of word-initial full glottal stops vs. no voicing irregularity. The results indicate that prominence and...

Let Γ(G) be a set of all simple graphs of order n and sizem, without isolated vertices, with vertex degree sequence d1 ≥ d2 ≥ ·· · ≥ dn > 0. A graph G is regular if and only if d1 = d2 = · · ·= dn. Each mapping Irr : Γ(G) 7→ [0,+∞) with the property Irr(G) = 0 if and only if G is regular, is referred to as irregularity measure of graph. In this paper we introduce some new irregularity measures ...

We propose two alternative measures of the local irregularity of a graph in terms of its vertex degrees and relate these measures to the order and the global irregularity of the graph measured by the difference of its maximum and minimum vertex degree.