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Vertex-Transitive Graphs and Accessibility

โœ Scribed by C. Thomassen; W. Woess


Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
929 KB
Volume
58
Category
Article
ISSN
0095-8956

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๐Ÿ“œ SIMILAR VOLUMES


Long cycles in vertex-transitive graphs
โœ Lรกszlรณ Babai ๐Ÿ“‚ Article ๐Ÿ“… 1979 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 192 KB

## Abstract We prove that every connected vertexโ€transitive graph on __n__ โ‰ฅ 4 vertices has a cycle longer than (3__n__)^1/2^. The correct order of magnitude of the longest cycle seems to be a very hard question.

Vertex-transitive graphs: Symmetric grap
โœ Peter Lorimer ๐Ÿ“‚ Article ๐Ÿ“… 1984 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 642 KB

Let G be a group acting symmetrically on a graph 2, let G, be a subgroup of G minimal among those that act symmetrically on 8, and let G2 be a subgroup of G, maximal among those normal subgroups of GI which contain no member except 1 which fixes a vertex of Z. The most precise result of this paper i

Vertex-transitive graphs that are not Ca
โœ McKay, Brendan D.; Praeger, Cheryl E. ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 881 KB

The Petersen graph on 10 vertices is the smallest example of a vertex-transitive graph that is not a Cayley graph. In 1983, D. MaruSiE asked, "For what values of n does there exist such a graph on n vertices?" We give several new constructions of families of vertex-transitive graphs that are not Cay

On cubic non-Cayley vertex-transitive gr
โœ Klavdija Kutnar,; Dragan Maruลกiฤ;; Cui Zhang ๐Ÿ“‚ Article ๐Ÿ“… 2011 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 197 KB

## Abstract In 1983, the second author [D. Maruลกiฤ, Ars Combinatoria 16B (1983), 297โ€“302] asked for which positive integers __n__ there exists a nonโ€Cayley vertexโ€transitive graph on __n__ vertices. (The term __nonโ€Cayley numbers__ has later been given to such integers.) Motivated by this problem,

The maximum genus of vertex-transitive g
โœ Martin ล koviera; Roman Nedela ๐Ÿ“‚ Article ๐Ÿ“… 1989 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 911 KB

The maximum genus of all vertex-transitive graphs is computed. It is proved that a k-valent vertex-transitive graph of girth g is upper-embeddable whenever k 3 4 or g 2 4. Non-upper-embeddable vertex-transitive graphs are characterized. A particular attention is paid to Cayley graphs. Groups for wh

Cubic vertex-transitive graphs of order
โœ Jin-Xin Zhou; Yan-Quan Feng ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 166 KB

A graph is vertex-transitive or symmetric if its automorphism group acts transitively on vertices or ordered adjacent pairs of vertices of the graph, respectively. Let G be a finite group and S a subset of G such that 1 / โˆˆ S and S = {s -1 | s โˆˆ S}. The Cayley graph Cay(G, S) on G with respect to S