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Characterization and enumeration of hypotraversable graphs

Published online by Cambridge University Press:  17 April 2009

S.P. Mohanty  and
Daljit Rao
S.P. Mohanty
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur, Uttar Pradesh, India.
Daljit Rao
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur, Uttar Pradesh, India.
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Abstract

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A graph G on p ≥ 2 vertices is said to be hypotraversable if G is not traversable but G − v is traversable, that is, G − v has an open trail which contains all the vertices and edges of G − v, for each vertex v of G. In this paper we first characterize hypotraversable graphs and then, using this characterization, obtain a complete enumeration of these graphs on p vertices for each positive integer p.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 3 , June 1979 , pp. 437 - 445
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Chartrand, Gary, Kapoor, S.F. and Kronk, Hudson V., “A sufficient condition for n-connectedness of graphs”, Mathematika 15 (1968), 51–52.CrossRefGoogle Scholar
[2]Chvátal, V., “Flip-flops in hypohamiltonian graphs”, Canad. Math. Bull. 16 (1973), 33–41.CrossRefGoogle Scholar
[3]Doyen, Jean and Diest, Viviane Van, “New families of hypohamiltonian graphs”, Discrete Math. 13 (1975), 225–236.CrossRefGoogle Scholar
[4]Herz, J.-C., Duby, J.-J., Vigué, F., “Recherche systématique des graphes hypohamiltoniens”, Theory of graphs, 153–159 (international Symposium Theorie des Graphes, International Computation Centre (Centre International de Calcul), Rome, 1966. Gordon and Breach, New York; Dunod, Paris; 1967).Google Scholar
[5]Kapoor, S.P., “Hypo-eulerian and hypo-traversable graphs”, Elem. Math. 28 (1973), 111–116.Google Scholar
[6]Lindgren, W.F., “An infinite class of hypohamiltonian graphs”, Amer. Math. Monthly 74 (1967), 1087–1089.CrossRefGoogle Scholar
[7]Thomassen, Carsten, “Hypohamiltonian and hypotraceable graphs”, Discrete Math. 9 (1974), 91–96.CrossRefGoogle Scholar
[8]Thomassen, Carsten, “Planar and infinite hypohamiltonian and hypotraceable graphs”, Discrete Math. 14 (1976), 377–389.CrossRefGoogle Scholar