Two-sided Cayley graphs
Abstract
We introduce a family of graphs that generalises the class of Cayley graphs. For non-empty subsets L, R of a group G, the two-sided Cayley graph 2SC(G;L,R) is the directed graph with vertex set G and an arc from x to y if and only if y=a^{-1}xb for some a in L and b in R. Thus, in common with Cayley graphs, two-sided Cayley graphs may be useful to model networks as the same routing and communication scheme can be implemented at each vertex. We determine when two-sided Cayley graphs are simple undirected graphs, and give sufficient conditions for them to be connected, vertex-transitive, or Cayley graphs. Several open problems are posed. Many examples are given, including one on 12 vertices with connected components of sizes 4 and 8.
Cite
@article{arxiv.1401.2741,
title = {Two-sided Cayley graphs},
author = {Moharram N. Iradmusa and Cheryl E. Praeger},
journal= {arXiv preprint arXiv:1401.2741},
year = {2014}
}
Comments
15 pages, 1 figure