A classification of pentavalent arc-transitive bicirculants
نویسندگان
چکیده
منابع مشابه
Arc-transitive Pentavalent Graphs of Order 4pq
This paper determines all arc-transitive pentavalent graphs of order 4pq, where q > p > 5 are primes. The cases p = 1, 2, 3 and p = q is a prime have been treated previously by Hua et al. [Pentavalent symmetric graphs of order 2pq, Discrete Math. 311 (2011), 2259-2267], Hua and Feng [Pentavalent symmetric graphs of order 8p, J. Beijing Jiaotong University 35 (2011), 132-135], Guo et al. [Pentav...
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A graph X is k-arc-transitive if its automorphism group acts transitively on the set of it-arcs of X. A circulant is a Cayley graph of a cyclic group. A classification of 2-arc-transitive circulants is given.
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The well-known Petersen G(5, 2) admits a semi-regular automorphism α acting on the vertex set with two orbits of equal size. This makes it a bicirculant. It is shown that trivalent bicirculants fall into four classes. Some basic properties of trivalent bicirculants are explored and the connection to combinatorial and geometric configurations are studied. Some analogues of the polycirculant conj...
متن کاملA census of 4-valent half-arc-transitive graphs and arc- transitive digraphs of valence two
A complete list of all connected arc-transitive asymmetric digraphs of in-valence and out-valence 2 on up to 1000 vertices is presented. As a byproduct, a complete list of all connected 4-valent graphs admitting a 12 -arc-transitive group of automorphisms on up to 1000 vertices is obtained. Several graph-theoretical properties of the elements of our census are calculated and discussed.
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A circulant is a Cayley digraph over a finite cyclic group. The classification of arc-transitive circulants is shown. The result follows from earlier descriptions of Schur rings over cyclic groups.
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2014
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-014-0548-z