The total irregularity of a graph

Graph Theory 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 eleme...

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Bibliographic Details
Published in:	Discrete mathematics and theoretical computer science Vol. 16 no. 1; no. Graph Theory; pp. 201 - 206
Main Authors:	Abdo, Hosam, Brandt, Stephan, Dimitrov, D.
Format:	Journal Article
Language:	English
Published:	Nancy DMTCS 01.01.2014 American Mathematical Society Discrete Mathematics & Theoretical Computer Science
Subjects:	[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] Combinatorics Computer Science Discrete Mathematics Graphs the irregularity of a graph the total irregularity of a graph extremal graphs the irregularity of a graph the total irregularity of a graph extremal graphs
ISSN:	1365-8050, 1462-7264, 1365-8050
Online Access:	Get full text
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Summary:	Graph Theory 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.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.1263