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Weakly clique irreducibility of NEPS of two graphs. (English) Zbl 1293.05321

Summary: 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.

MSC:

05C76 Graph operations (line graphs, products, etc.)
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
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