On the monophonic convexity number of the complementary prisms

08/22/2022

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by   Neethu P. K., et al.

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A set S of vertices of a graph G is monophonic convex if S contains all the vertices belonging to any induced path connecting two vertices of S. The cardinality of a maximum proper monophonic convex set of G is called the monophonic convexity number of G. The complementary prism GG̅ of G is obtained from the disjoint union of G and its complement G̅ by adding the edges of a perfect matching between them. In this work, we determine the monophonic convexity number of the complementary prisms of all graphs.