Generating sequences of clique-symmetric graphs via Eulerian digraphs

Abstract

Let { G p 1 , G p 2 , … } be an infinite sequence of graphs with G pn having pn vertices. This sequence is called K p -removable if G p 1 ≅ K p , and G pn - S ≅ G p ( n - 1 ) for every n ⩾ 2 and every vertex subset S of G pn that induces a K p . Each graph in such a sequence has a high degree of symmetry: every way of removing the vertices of any fixed number of disjoint K p 's yields the same subgraph. Here we construct such sequences using componentwise Eulerian digraphs as generators. The case in which each G pn is regular is also studied, where Cayley digraphs based on a finite group are used.