For a subset S of a group G such that 1 / β S and S = S -1 , the associated Cayley graph Cay(G, S) is the graph with vertex set G such that {x, y} is an edge if and only if yx -1 β S. Each Ο β Aut(G) induces an isomorphism from Cay(G, S) to the Cayley graph Cay(G, S Ο ). For a positive integer m, th
On the isomorphism problem for a family of cubic metacirculant graphs
β Scribed by Ngo Dac Tan
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 589 KB
- Volume
- 151
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
In this paper an isomorphism testing algorithm for graphs in the family of all cubic metacirculant graphs with non-empty first symbol So is given. The time complexity of this algorithm is also evaluated.
π SIMILAR VOLUMES
In this short paper, we give a positive answer to a question of C. D. Godsil (1983, Europ. J. Combin. 4, 25 32) regarding automorphisms of cubic Cayley graphs of 2-groups: ``If Cay(G, S) is a cubic Cayley graph of a 2-group G and A=Aut Cay(G, S), does A 1 {1 imply Aut(G, S){1?'' 1998 Academic Press
## Abstract We investigate a family of graphs relevant to the problem of finding large regular graphs with specified degree and diameter. Our family contains the largest known graphs for degree/diameter pairs (3, 7), (3, 8), (4, 4), (5, 3), (5, 5), (6, 3), (6, 4), (7, 3), (14, 3), and (16, 2). We a
## Abstract Every 3βconnected planar, cubic, triangleβfree graph with __n__ vertices has a bipartite subgraph with at least 29__n__/24βββ7/6 edges. The constant 29/24 improves the previously best known constant 6/5 which was considered best possible because of the graph of the dodecahedron. Example
Given any prime p, there are two non-isomorphic groups of order p2. We determine precisely when a Cayley digraph on one of these groups is isomorphic to a Cayley digraph on the other group, Namely, let X = Cay(G: T) be a Cayley digraph on a group G of order p2 with generating set T. We prove that X