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On the hamiltonian product of graphs

Published online by Cambridge University Press:  17 April 2009

V. Krishnamoorthy
V. Krishnamoorthy
Affiliation:
Department of Mathematics, Indian Institute of Technology, Madras, Tamil Nadu, India.
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Abstract

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Let G1 and G2 be graphs and h1, h2 be hamiltonian paths (h-paths) in G1 and G2 respectively. The hamiltonian product (G1, h2)*(G2, h2) was defined by Holton. If a hamiltonian cycle exists in G2, it can give rise to 2nh-paths. Peckham conjectured that (G1, h1)*(G2, h2)≡(G1, h1)*(G2, h3) where h2 and h3 are any two of these 2nh-paths of G2. He has proved the validity of this conjecture for those h2, h3 where h3 is obtainable from h2 by a rotation along the h-cycle of G2. Here we disprove this conjecture for those h2, h3 where one is obtained from the other by a reflection of the h-cycle.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 2 , April 1976 , pp. 289 - 292
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Peckham, I.A., “The hamiltonian product of graphs”, Combinatorial mathematics, 86–95 (Proc. Second Austral. Conf. Lecture Notes in Mathematics, 403. Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar