Strong (Weak) Full cc-domination in a Graph

A clique is a maximal complete subgraph of a graph. The cc-degree (clique-clique degree) of a clique K (dcc(K)) is the number of cliques adjacent to K. A clique C strongly clique-dominates a clique K if C is adjacent to K and dcc(C) ≥ dcc(K). Let C(G) be the set of all cliques in a graph G. A set S...

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Bibliographic Details
Published in:Engineering letters 2023-11, Vol.31 (4), p.1480
Main Authors: Laxmana, Anusha, Vinayaka, Sayinath Udupa Nagara, Bhat, Ravi Shankar, Nagaraja, Prathviraj
Format: Article
Language:English
Subjects:
Algorithms
Graph theory
Parameters
Set theory
Online Access:Get full text
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Summary:A clique is a maximal complete subgraph of a graph. The cc-degree (clique-clique degree) of a clique K (dcc(K)) is the number of cliques adjacent to K. A clique C strongly clique-dominates a clique K if C is adjacent to K and dcc(C) ≥ dcc(K). Let C(G) be the set of all cliques in a graph G. A set S ⊆ C(G) is a strong clique-clique dominating set (SCCDset) of G if every clique in C(G)-S is strongly clique-dominated by at least one clique in S. The strong clique-clique domination number γscc(G) is the cardinality of a smallest SCCD-set of G. Similarly, the weak clique-clique domination number γwcc(G) is defined. In this paper, we study some properties of these strong (weak) clique-clique domination parameters and obtain Gallaitype results. We present an algorithm to find γscc(G) (γwcc(G)) and obtain some bounds for the newly defined parameters. Further, we define and study clique-clique domination balanced graphs and clique-posets.
ISSN:1816-093X
1816-0948