The Minimal Total Irregularity of Graphs

Abstract

In \cite{2012a}, Abdo and Dimitov defined the total irregularity of a graph $G=(V,E)$ as \hskip3.3cm $\mathrm{ir}{\mathrm{r}}_{\mathrm{t}}$$(G)=\frac{1}{2}{\sum }_{u,v\in V}|d_G(u)-d_G(v)|,$ \noindent where $d_G(u)$ denotes the vertex degree of a vertex $u\in V$. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on $n$ vertices, and propose an open problem for further research.

13 pages, 4 figures

Cited by in corpus (1)

• Certain Types of Total Irregularities of Graphs and Digraphs