On vertex-transitive, non-Cayley graphs of order pqr
نویسندگان
چکیده
منابع مشابه
Cubic Vertex-Transitive Non-Cayley Graphs of Order 8p
A graph is vertex-transitive if its automorphism group acts transitively on its vertices. A vertex-transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this paper, the cubic vertextransitive non-Cayley graphs of order 8p are classified for each prime p. It follows from this classification that there are two sporadic and two infini...
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A construction is given for an infinite family {0n} of finite vertex-transitive non-Cayley graphs of fixed valency with the property that the order of the vertex-stabilizer in the smallest vertex-transitive group of automorphisms of 0n is a strictly increasing function of n. For each n the graph is 4-valent and arc-transitive, with automorphism group a symmetric group of large prime degree p> 2...
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We present a new construction of infinite families of (finite as well as infinite) vertex-transitive graphs that are not Cayley graphs; many of these turn out even to be arc-transitive. The construction based on representing vertex-transitive graphs as coset graphs of groups, and on a simple but powerful necessary arithmetic condition for Cayley graphs. Vertex-transitive graphs are interesting ...
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For any d ≥ 5 and k ≥ 3 we construct a family of Cayley graphs of degree d, diameter k, and order at least k((d−3)/3)k. By comparison with other available results in this area we show that, for all sufficiently large d and k, our family gives the current largest known Cayley graphs of degree d and diameter k.
متن کاملNon-Cayley Vertex-Transitive Graphs of Order Twice the Product of Two Odd Primes
For a positive integer n, does there exist a vertex-transitive graph r on n vertices which is not a Cayley graph, or, equivalently, a graph r on n vertices such that Aut F is transitive on vertices but none of its subgroups are regular on vertices? Previous work (by Alspach and Parsons, Frucht, Graver and Watkins, MaruSic and Scapellato, and McKay and the second author) has produced answers to ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(97)00149-0