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Another characterization of hypercubes

Authors
Journal
Discrete Mathematics
0012-365X
Publisher
Elsevier
Publication Date
Volume
39
Issue
2
Identifiers
DOI: 10.1016/0012-365x(82)90139-x

Abstract

Résumé Nous montrons que dans la classe des graphes connexes tels que deux arêtes incidentes quelconques appartiennent á un et un seul quadrilatére, les hypercubes finis sont les graphes de degré minimum n fini et possédant 2 n sommets. The following theorem 1 is proved: Let C be the class connected graphs such that each pair of distinct adjacent edges lies in exactly one 4-cycle. Then G in C is a finite hypercube ifthe minimum degree δ of G is finite and 2 | V( G)| = 2 δ .

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