2025/01/26 by Anand, Bijo S., V., Ullas Chandran S., Dayap, Jonecis A. +2
#05C38 #05C76 #05C99 #52A01 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.15524
Let G = (V, E) be a simple undirected graph. A set C ⊆ V(G) is weakly convex of graph G if for every two vertices u,v∈ G, there exists a u-v geodesic whose vertices are in C. A set C ⊆ V is an outer-weakly convex dominating set if it is dominating set and every vertex not in C is adjacent to some vertex in C and a set V(G)∖ C is weakly convex. The outer-weakly convex domination number of graph G, denoted by \widetilde γwcon(G), is the minimum cardinality of an outer-weakly convex dominating vertex set of graph G. In this paper, we determined the outer-weakly convex domination number of two graphs under the cartesian, strong and lexicographic products, and discuss some important combinatorial findings.