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The complementary product of two graphs. (English) Zbl 1155.05051
The authors introduce a new type of graph product, called the complementary product and study distance, independence and domination parameters of complementary prism resulting from this operation. Roughly speaking the complementary prism of a graph \(G\) is a copy of \(G\) and a copy of its complement with a matching between the corresponding vertices. The complementary product generalizes the concept of a cartesian product. In section 2 degrees and distance are investigated. Section 3 presents some results concerning vertex independence numbers and clique numbers. Results about domination number and total domination number are obtained in section 4. The paper is concluded with some open questions and problems.

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C99 Graph theory