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A characterization of panconnected graphs satisfying a local ore-type condition

✍ Scribed by Asratian, A. S.; H�ggkvist, R.; Sarkisian, G. V.

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
491 KB
Volume
22
Category
Article
ISSN
0364-9024

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✦ Synopsis

It is well known that a graph G of orderp 2 3 is Hamilton-connected if d(u) +d(v) 2 p + 1 for each pair of nonadjacent vertices u and w. In this paper we consider connected graphs G of order at least 3 for which

where N ( z ) denote the neighborhood of a vertex z. We prove that a graph G satisfying this condition has the following properties: (a) For each pair of nonadjacent vertices z, y of G and for each integer k , d(z, y) I k I IV(G)l -1, there is an zy path of length k . (b) For each edge xy of G and for each integer k (excepting maybe one k E {3,4}) there is a cycle of length k containing zy.

Consequently G is panconnected (and also edge pancyclic) if and only if each edge of

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