Title: |
Outer-clique Weakly Convex Domination in Graphs |
Authors: |
Cherlyn S. Dado, Enrico L. Enriquez |
Source: |
International Journal of Latest Engineering Research and Applications, pp 01 - 05, Vol 11 - No. 04, 2026 |
Abstract: |
Let G be a connected simple graph. A subset S of V(G) is a dominating set of G if for every v∈V(G)\S, there exists x∈S such that xv∈E(G). A subset C of V(G) is called a weakly convex set of G if for every two vertices u,v∈C, there exists a u−v geodesic whose vertices belong to C. A dominating set of S which is also weakly convex is called a weakly convex dominating set of G. A weakly convex dominating set S is an outer-clique weakly convex dominating set of G if the graph {V(G)\S} induced by V G \S is complete. The minimum cardinality of an outer-clique weakly convex dominating set of G, denoted by γcwc G , is called the outer-clique weakly convex domination number of G. In this paper, we initiate the study of the concept and provide the outer-clique weakly convex domination numbers in somespecial graphs. Further, we show the sufficient conditions of an outer-clique weakly convex dominating set in the join of two nontrivial connected graphs. |
Kaywords: |
dominating, weakly convex, outer-clique, outer-clique weakly convex, join |
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DOI: |
10.56581/IJLERA.11.04.01-05 |
Title: |
Disjoint Connected Domination in Graphs |
Authors: |
Romelyn M. Dumanhog, Enrico L. Enriquez |
Source: |
International Journal of Latest Engineering Research and Applications, pp 06 - 12, Vol 11 - No. 04, 2026 |
Abstract: |
Let G be a connected simple graph. A subset S of V(G) is a dominating set of G if for every v ϵ V(G)∖S, there exists x ϵ S such that xv ϵ E(G). A connected dominating set C of a graph G is a dominating set of G such that the subgraph induced by the vertices of C in G is connected. Let C be a minimum connected dominating set of G. The connected dominating set S⊆V(G)∖Cis called an inverse connected dominating set of Gwith respect to C. A disjoint connected dominating set of G is the set D=C∪S⊆V(G). The minimum cardinality of a disjoint connected dominating set of G, denoted by γγc(G), is called the disjoint connected domination number of G. In this paper, we initiate the study of the concept and give the domination number of special graphs. Further, we show the characterization of the disjoint connected dominating set in the join of two nontrivial connected graphs. |
Kaywords: |
dominating, connected, disjoint, disjoint connected, join |
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DOI: |
10.56581/IJLERA.11.04.06-12 |
