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On randomly 3-axial graphs

Published online by Cambridge University Press:  17 April 2009

Yousef Alavi ,
Sabra S. Anderson ,
Gary Chartrand  and
S.F. Kapoor
Yousef Alavi
Affiliation:
Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008, USA.
Sabra S. Anderson
Affiliation:
Department of Mathematics, University of Minnesota, Duluth, Minnesota 55812, USA.
Gary Chartrand
Affiliation:
Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008, USA.
S.F. Kapoor
Affiliation:
Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008, USA.
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Abstract

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A graph G, every vertex of which has degree at least three, is randomly 3-axial if for each vertex v of G, any ordered collection of three paths in G of length one with initial vertex v can be cyclically randomly extended to produce three internally disjoint paths which contain all the vertices of G. Randomly 3-axial graphs of order p > 4 are characterized for p ≢ 1 (mod 3), and are shown to be either complete graphs or certain regular complete bipartite graphs.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 2 , April 1982 , pp. 187 - 206
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Burns, David, Chartrand, Gary, Kapoor, S.F. and Saba, Farrokh, “Randomly k-axial graphs”, Bull. Austral. Math. Soc. 23 (1981), 143–156.Google Scholar
[2]Chartrand, Gary and Kronk, Hudson V., “Randomly traceable graphs”, SIAM J. Appl. Math. 16 (1968), 696–700.CrossRefGoogle Scholar