Distance monotonicity and a new characterization of Hamming graphs

Aouchiche, Mustapha

doi:10.1016/j.ipl.2005.08.009

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Theorem 31 a Connected Graph G Is Interval Distance Monoto1

Introduction1

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2007

2008

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Cited by 2 publications

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“…The following one can be easily proved by Theorem 2.6(1) and (2) and was described in a recent paper [2]. [2]). Let G be an interval distance monotone graph.…”

Section: Theorem 31 a Connected Graph G Is Interval Distance Monotomentioning

confidence: 76%

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A characterization of the interval distance monotone graphs

Zhang

Wang

2007

Discrete Mathematics

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A simple connected graph G is said to be interval distance monotone if the interval I (u, v) between any pair of vertices u and v in G induces a distance monotone graph. Aïder and Aouchiche [Distance monotonicity and a new characterization of hypercubes, Discrete Math. 245 (2002) 55-62] proposed the following conjecture: a graph G is interval distance monotone if and only if each of its intervals is either isomorphic to a path or to a cycle or to a hypercube. In this paper we verify the conjecture.

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“…The following one can be easily proved by Theorem 2.6(1) and (2) and was described in a recent paper [2]. [2]). Let G be an interval distance monotone graph.…”

Section: Theorem 31 a Connected Graph G Is Interval Distance Monotomentioning

confidence: 76%

“…Aïder and Aouchiche [1,2] proposed a conjecture: a graph G is interval distance monotone if and only if each of its intervals is either isomorphic to a path or to a cycle or to a hypercube. In this paper we show that this conjecture is correct (see Theorem 3.1).…”

Section: Introductionmentioning

confidence: 99%