Abdo, Hosam and Brandt, Stephan and Dimitrov, D. - The total irregularity of a graph

dmtcs:1263 - Discrete Mathematics & Theoretical Computer Science, April 4, 2014, Vol. 16 no. 1 (in progress)
The total irregularity of a graph

Authors: Abdo, Hosam and Brandt, Stephan and Dimitrov, D.

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 (in progress)
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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