2020/04/09 by P. K. Neethu, K., Neethu P., Ullas Chandran S. +1
Computer Science · Mathematics · #05C12 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2004.04638
openalex publication_date 2020/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A set of vertices S of a graph G is a (geodesic)convex set, if S contains all the vertices belonging to any shortest path connecting between two vertices of S. The cardinality of maximum proper convex set of G is called the convexity number, con(G) of G. The complementary prism GG of G is obtained from the disjoint union of G and its complement G by adding the edges of a perfect matching between them. In this work, we examine the convex sets of the complementary prism of a tree and derive formulas for the convexity numbers of the complementary prisms of all trees.