2022/08/22 by P. K. Neethu, K., Neethu P., Ullas Chandran S.V. +2 · 1 citation
Computer Science · Materials Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Photochromic and Fluorescence Chemistry
paper · pdf · doi:10.48550/arxiv.2208.10215
openalex publication_date 2022/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 monophonic interval of a set S of vertices of G is the set S together with every vertex belonging to any induced path connecting two vertices of S. The cardinality of a minimum set S ⊆ V(G) whose monophonic interval is V(G) is called the monophonic number of G. The monophonic convex hull of a set S of vertices of G is the smallest monophonic convex set containing S in G. The cardinality of a minimum set S ⊆ V(G) whose monophonic convex hull is V(G) is called the monophonic hull number 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 determine the monophonic convexity number, the monophonic number, and the monophonic hull number of the complementary prisms of all graphs.