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- W3204197862 abstract "This paper discusses a family of graphs, called Praeger-Xu graphs and denoted PX(n,k) here, introduced by C.E. Praeger and M.-Y. Xu in 1989. These tetravalent graphs are distinguished by having large symmetry groups; their vertex-stabilizers can be arbitrarily larger than the number of vertices in the graph. This paper does the following: (1) exhibits a connection between vertex-transitive groups of symmetries in a Praeger-Xu graph and certain linear codes, (2) characterizes those linear codes, (3) characterizes Praeger-Xu graphs PX(n,k) which are Cayley, (4) shows that every PX(n,k) is quasi-Cayley, and (5) constructs an infinite family of Praeger-Xu graphs in which a smallest vertex-transitive group of symmetries has arbitrarily large vertex-stabiliser." @default.
- W3204197862 created "2021-10-11" @default.
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- W3204197862 date "2022-01-01" @default.
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- W3204197862 title "On the Cayleyness of Praeger-Xu graphs" @default.
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- W3204197862 doi "https://doi.org/10.1016/j.jctb.2021.09.003" @default.
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