Kemeny’s constant and Kirchhoffian indices for conjoined highly symmetric graphs

Abstract

Bouquet graphs consist of the conjoining at a single vertex of a collection of (possibly distinct) pieces which are highly symmetric graphs. We find closed form formulas for Kemeny’s constant and two Kirchhoffian indices for bouquet graphs in terms of the parameters of the component pieces. We also provide some general results on highly symmetric graphs, and prove in particular that regular edge-transitive graphs are highly symmetric.