Some Studies on Clique-free Sets of a Graph Using Clique Degree Conditions

Cliques are maximal complete subgraphs of a graph. A vertex v is said to vc-cover a clique C if v is in the clique C. A set S of vertices of a graph G is called a vccovering set of G if every clique of G is vc-covered by some vertex in S. The cardinality of the smallest vc-covering set of G is calle...

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Veröffentlicht in:IAENG international journal of applied mathematics 2024-08, Vol.54 (8), p.1689-1693
Hauptverfasser: Laxmana, Anusha, Vinayaka, Sayinath Udupa Nagara, Madhusudanan, Vinay, Nagaraja, Prathviraj
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Sprache:eng
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Zusammenfassung:Cliques are maximal complete subgraphs of a graph. A vertex v is said to vc-cover a clique C if v is in the clique C. A set S of vertices of a graph G is called a vccovering set of G if every clique of G is vc-covered by some vertex in S. The cardinality of the smallest vc-covering set of G is called the vc-covering number, denoted as αvc(G). In this paper, we define new parameters such as strong (weak) vccovering number and strong (weak) clique-free number, and we establish a relationship between them. We present an algorithm to find these numbers and obtain some bounds for the newly defined parameters. In addition, we define a partial order on the vertex set of a graph using clique degree conditions and study some of its properties.
ISSN:1992-9978
1992-9986