Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-17T00:17:57.671Z Has data issue: false hasContentIssue false

Constructing graphs which are ½-transitive

Published online by Cambridge University Press:  09 April 2009

Brian Alspach
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, B. C. V5A 1S6, Canada
Dragan Marušič
Affiliation:
Insttitut za Mathematiko, Fiziko in Mehaniko, Jadranska 19, 61111 Ljublijana, Slovenija, Yugoslavia
Lewis Nowitz
Affiliation:
Apartment 9Q, 275 West 96th Street, New York 10025
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An infinite family of vertex-and edge-transitive, but not arc-transitive, graphs of degree 4 is constructed.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Alspach, B. and Parsons, T. D., ‘A construction for vertex-transitive graphs’, Canad. J. Math. 34 (1982), 307318.CrossRefGoogle Scholar
[2]Alspach, B., ‘On hamiltonian cycle in metacirculant graphs’, Ann. Discrete Math. 15 (1982), 17.Google Scholar
[3]Biggs, N., Algebraic graph theory (Cambridge University Press, Cambridge, 1974).CrossRefGoogle Scholar
[4]Bouwer, I. Z., ‘Vertex and edge-transitive but not 1-transitive graphs’, Canad. Math. Bull. 13 (1970), 231237.CrossRefGoogle Scholar
[5]Cheng, Y. and Oxley, J., ‘On weakly symmetric graphs of order twice a prime’, J. Combin. Theory Ser. B 42 (1987), 196211.CrossRefGoogle Scholar
[6]Folkman, J., ‘Regular line-symmetric graphs’, J. Combin. Theory 3 (1967), 215232.CrossRefGoogle Scholar
[7]Holt, D. F., ‘A graph which is edge-transitive but not arc-transitive’, J. Graph Theory 5 (1981), 201204.CrossRefGoogle Scholar
[8]Holton, D., ‘Research Problem9’, Discrete Math. 38 (1982), 125.Google Scholar
[9]Marušič, D., ‘Vertex transitive graphs and digraphs of order p k’, Ann. Discrete Math. 27 (1985), 115128.Google Scholar
[10]McKay, B. D., ‘Transitive graphs with fewer than 20 vertices’, 33 (1979), 1101–1121.Google Scholar
[11]McKay, B. D. and Royle, G. F., ‘The transitive graphs with at most 26 vertices’, Ars Combin. 30 (1990), 161176.Google Scholar
[12]Praeger, C. E. and Y, Xu M., ‘Vertex primitive graphs of order a product of two distinct primes’, preprint.Google Scholar
[13]Praeger, C. E. and Royle, G. F., ‘Constructing the vertex transitive graphs of order 24’, J. Symbolic Comput. 8 (1989), 309326.Google Scholar
[14]Turner, J., ‘Point symmetric graphs with a prime number of points’, J. Combin. Theory 3 (1967), 136145.CrossRefGoogle Scholar
[15]Tutte, W. T., Connectivity in graphs (University of Toronto Press, Toronto, 1966).CrossRefGoogle Scholar