A note on partial Cayley graphs (Q685657)

A vertex-transitive bipartite graph of degree 7 and diameter 3 with 78 vertices is presented. The construction of this graph is generalized to the construction of bipartite graphs with high symmetry. Let \(\Gamma\) be a group with a subgroup \(\Gamma'\) and a subset \(S\) of \(\Gamma\) disjoint to \(\Gamma'\). Then \(G\) is defined to be the bipartite graph whose vertices are the elements of \(\Gamma\) and whose edges are the pairs \((x,xs)\) with \(x\in \Gamma'\) and \(s\in S\). \(G\) is called a partial Cayley graph. The structure of such graphs is investigated.