Well irredundant graphs

doi:10.1016/0166-218X(94)00073-9

Discrete Applied Mathematics

Volume 63, Issue 3, 8 December 1995, Pages 267-276

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Abstract

A vertex x in a subset X of vertices of a graph is redundant if its closed neighbourhood is contained in the union of closed neighbourhoods of vertices of X − x. This paper describes the structure of bipartite graphs, chordal graphs and graphs of girth at least five in which every maximal set of vertices having no redundancies is maximum.

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^∗: Present address: Faculty of Applied Physics and Mathematics, Gdańsk Technical University, Narutowicza 11/12, 80-952 Gdańsk, Poland. This research has been carried out at the Technical University of Aachen and completed at the Aalborg University. The support of the Heinrich Hertz Foundation is gratefully acknowledged.