On Generalizations of the Petersen Graph and the Coxeter Graph
In this note we consider two related infinite families of graphs, which generalize the Petersen and the Coxeter graph. The main result proves that these graphs are cores. It is determined which of these graphs are vertex/edge/arc-transitive or distance-regular. Girths and odd girths are computed. A problem on hamiltonicity is posed.
A Corrigendum for this paper was added on August 19, 2017.