Title: |
Weakly Convex Restrained Domination on Graphs |
Authors: |
Jessavelle S. Baret, Enrico L. Enriquez |
Source: |
International Journal of Latest Engineering Research and Applications, pp 01 - 08, Vol 11 - No. 05, 2026 |
Abstract: |
Let G be a connected simple graph. A dominating set S⊆V(G) is a restrained dominating set if every vertex not in S is adjacent to a vertex inSand to a vertex in V G ∖S. Alternatively, a dominating setS⊆V(G) is a restrained dominating set if N S =V(G) and V G ∖S has no isolated vertices. A restrained dominating setSis called a weakly convex restrained dominating setif for every two vertices u,v∈S, there exists a u−v geodesic whose vertices belong to S. The minimum cardinality of a weakly convex restrained dominating set of G, denoted by γwcr(G), is called the weakly convex restrained domination number of G. This paper initiates the study of weakly convex restrained domination in graphs and determines the weakly convex restrained domination number of some special graphs. Furthermore, it presents a characterization of the weakly convex restrained dominating set in the join and corona of two nontrivial connected graphs. |
Kaywords: |
dominating set, restrained dominating set, weakly convex dominating set, weakly convex restrained dominating set |
 |
Download Full Article |
DOI: |
10.56581/IJLERA.11.05.01-08 |
