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  1. Home > Articles & Issues >
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  3. The total irregulari ...
Article

The total irregularity of a graph

Hosam Abdo (1), Stephan Brandt (2), D. Dimitrov (1)
(1) Institut für Informatik [Berlin]
(2) Department of Mathematics and Computer Science [Odense]
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September 30, 2012
Published on
April 3, 2014
Last modified on
March 31, 2025
Volume 16
vol. 16:1
Graph Theory
DOI
10.46298/dmtcs.1263
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https://about.hal.science/hal-authorisation-v1
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The total irregularity of a graph

Hosam Abdo (1), Stephan Brandt (2), D. Dimitrov (1)
(1) Institut für Informatik [Berlin]
(2) Department of Mathematics and Computer Science [Odense]
Abstract
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.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • the irregularity of a graph the total irregularity of a graph extremal graphs
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