1/2-Transitive Graphs of Order 3 p
Brian Alspach
and Ming-Yao Xu
DOI: 10.1023/A:1022466626755
Abstract
A graph X is called vertex-transitive, edge-transitive, or arc-transitive, if the automorphism group of X acts transitively on the set of vertices, edges, or arcs of X, respectively. X is said to be 1/2-transitive, if it is vertex-transitive, edge-transitive, but not arc-transitive.
In this paper we determine all 1/2-transitive graphs with 3 p vertices, where p is an odd prime. (See Theorem 3.4.)
Pages: 347–355
Keywords: 1/2-transitive graph; metacirculant; factor graph
Full Text: PDF
References
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2. Alspach, B. and Parsons, T.D., "A construction for vertex-transitive graphs," Canad. J. Math. 34 (1982), 307-318.
3. Biggs, N., Algebraic Graph Theory, Cambridge University Press, 1974.
4. Cameron, P.J., "Finite permutation groups and finite simple groups," Bull. London Math. Soc. 13 (1981), 1-22. 355
5. Chartrand, G. and Lesniak, L., Graphs & Digraphs, Wadsworth and Brooks/Cole, Monterey, 1979.
6. Huppert, B., Endliche Gruppen 1, Springer-Verlag, 1967.
7. Wang, R.J. and Xu, M.Y., "A classification of symmetric graphs of order 3p," J. Combin. Theory Ser. B, 58 (1993), 197-216.
8. Wielandt, H., Finite Permutation Groups, Academic Press, New York, 1964.
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