Results 11 to 20 of about 1,592 (153)
Classification of edge-transitive propeller graphs [PDF]
, 2022 In this paper, we introduce a family of tetravalent graphs called propeller graphs, denoted by $Pr_{n}(b,c,d)$. We then produce three infinite subfamilies and one finite subfamily of arc-transitive propeller graphs, and show that all such graphs are necessarily members of one of these four subfamilies, up to isomorphism.
Matthew C. Sterns
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Edge-transitive embeddings of complete graphs [PDF]
The Art of Discrete and Applied Mathematics, 2020 14 pages, 8 ...
Gareth A. Jones
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On graphs with edge-transitive automorphism groups [PDF]
Illinois Journal of Mathematics, 1984 We need some definitions from the paper under review. Hypothesis A. Let G be a group and \(M_ 1\) and \(M_ 2\) be finite subgroups of G such that: (1) \(G=\). (2) No non-trivial normal subgroup of G is contained in \(M_ 1\cap M_ 2\). (3) \(| M_ i/M_ 1\cap M_ 2| =2^{n_ i}+1\) for \(n_ i\geq 1\), \(i=1,2\), and \(n_ 1n_ 2>1\).
Bernd Stellmacher
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Strongly regular edge-transitive graphs
Ars Mathematica Contemporanea, 2009 In this paper, we examine the structure of vertex- and edge-transitive strongly regular graphs, using normal quotient reduction. We show that the irreducible graphs in this family have quasiprimitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group.
Joy Morris +2 more
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Recipes for Edge-Transitive Tetravalent Graphs [PDF]
, 2022 This paper is to accompany the Census of Edge-Transitive Tetravalent Graphs, available at jan.ucc.nau.edu/~swilson/C4FullSite/index.html, which is a collection of all known edge-transitive graphs of valence 4 up to 512 vertices. The Census contains information for each graph. This information includes parameters such as group order, diameter, girth etc.
Steve Wilson, Primož Potočnik
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Edge-Transitive Homogeneous Factorisations of Complete Graphs [PDF]
, 2022 This thesis concerns the study of homogeneous factorisations of complete graphs with edge-transitive factors. A factorisation of a complete graph $K_n$ is a partition of its edges into disjoint classes. Each class of edges in a factorisation of $K_n$ corresponds to a spanning subgraph called a factor.
Tian Khoon Lim
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Edge-transitive core-free Nest graphs [PDF]
Ars Mathematica Contemporanea, 2022 arXiv admin note: text overlap with arXiv:2111 ...
I. Kovács
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Edge-transitive graphs and combinatorial designs [PDF]
Involve, a Journal of Mathematics, 2019 A graph is said to be edge-transitive if its automorphism group acts transitively on its edges. It is known that edge-transitive graphs are either vertex-transitive or bipartite. In this paper we present a complete classification of all connected edge-transitive graphs on less than or equal to $20$ vertices.
Heather Newman +3 more
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On Edge Transitive Circulant Graphs [PDF]
Tokyo Journal of Mathematics, 1996 This paper classifies those circulant graphs for which both the graph and its complement are edge-transitive. The author shows that such a graph must be either a disjoint union of copies of a complete graph, or the complement of such a disjoint union, or a Paley graph on a prime number of vertices.
Hong Zhang
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Finite normal edge-transitive Cayley graphs [PDF]
Bulletin of the Australian Mathematical Society, 1999 An approach to analysing the family of Cayley graphs for a finite group G is given which identifies normal edge-transitive Cayley graphs as a sub-family of central importance. These are the Cayley graphs for G for which a subgroup of automorphisms exists which both normalises G and acts transitively on edges. It is shown that, for a nontrivial group G,
Cheryl E. Praeger
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