In this note a new measure of irregularity of a graph G is introduced. It is named the total irregularity of a graph and is defined as irr(t)(G) - 1/2 Sigma(u, v is an element of V(G)) vertical bar d(G)(u) - d(G)(v)vertical bar, where d(G)(u) denotes the degree of a vertex u is an element of V(G). All graphs with maximal total irregularity are determined. It is also shown that among all trees of the same order the star has the maximal total irregularity.

Source : oai:HAL:hal-01179217v1

Volume: Vol. 16 no. 1

Section: Graph Theory

Published on: April 4, 2014

Submitted on: October 1, 2012

Keywords: the irregularity of a graph the total irregularity of a graph extremal graphs,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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