Weakly clique irreducibility of NEPS of two graphs

摘要

A clique of a graph G is essential if it has an edge which does not belong to any other clique in G. A graph G is weakly clique irreducible if every edge in G belongs to at least one essential clique in G and is weakly clique reducible, otherwise. The closure property of weakly clique irreducible and reducible graphs under the noncomplete extended p-sums (NEPS) of two graphs are studied.