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

dmtcs:1263 - Discrete Mathematics & Theoretical Computer Science, April 4, 2014, Vol. 16 no. 1 - https://doi.org/10.46298/dmtcs.1263
The total irregularity of a graph

Authors: Hosam Abdo 1; Stephan Brandt 2; D. Dimitrov 1

  • 1 Institut für Informatik [Berlin]
  • 2 Department of Mathematics and Computer Science [Odense]

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.

Volume: Vol. 16 no. 1
Section: Graph Theory
Published on: April 4, 2014
Accepted on: July 23, 2015
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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