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arXiv · 1207.5267

The total irregularity of a graph

Hosam Abdo·Darko Dimitrov
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Abstract

In this note a new measure of irregularity of a simple undirected graph $G$ is introduced. It is named the total irregularity of a graph and is defined as $\irr_t(G) = 1/2\sum_{u,v \in V(G)} |d_G(u)-d_G(v)|$, where $d_G(u)$ denotes the degree of a vertex $u \in V(G)$. The graphs with maximal total irregularity are determined. It is also shown that among all trees of same order the star graph has the maximal total irregularity.

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Hosam Abdo, Darko Dimitrov. 2012-07-22. The total irregularity of a graph. https://arxiv.org/abs/1207.5267

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