Strong (Weak) Full cc-domination in a Graph

Anusha Laxmana; Sayinath Udupa Nagara Vinayaka; Ravi Shankar Bhat; Prathviraj Nagaraja

Strong (Weak) Full cc-domination in a Graph

Anusha Laxmana
, Sayinath Udupa Nagara Vinayaka^*
, Ravi Shankar Bhat
, Prathviraj Nagaraja

^*Corresponding author for this work

Manipal Institute of Technology, Manipal

Research output: Contribution to journal › Article › peer-review

Abstract

A clique is a maximal complete subgraph of a graph. The cc-degree (clique-clique degree) of a clique K (d_cc(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 d_cc(C) ≥ d_cc(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 (SCCD-set) 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 γ_scc(G) is the cardinality of a smallest SCCD-set of G. Similarly, the weak clique-clique domination number γ_wcc(G) is defined. In this paper, we study some properties of these strong (weak) clique-clique domination parameters and obtain Gallai-type results. We present an algorithm to find γ_scc(G) (γ_wcc(G)) and obtain some bounds for the newly defined parameters. Further, we define and study clique-clique domination balanced graphs and clique-posets.

Original language	English
Pages (from-to)	1480-1485
Number of pages	6
Journal	Engineering Letters
Volume	31
Issue number	4
Publication status	Published - 01-11-2023

All Science Journal Classification (ASJC) codes

General Engineering

Cite this

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title = "Strong (Weak) Full cc-domination in a Graph",

abstract = "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 (SCCD-set) 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 Gallai-type 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.",

author = "Anusha Laxmana and Vinayaka, \{Sayinath Udupa Nagara\} and Bhat, \{Ravi Shankar\} and Prathviraj Nagaraja",

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T1 - Strong (Weak) Full cc-domination in a Graph

AU - Laxmana, Anusha

AU - Vinayaka, Sayinath Udupa Nagara

AU - Bhat, Ravi Shankar

AU - Nagaraja, Prathviraj

PY - 2023/11/1

Y1 - 2023/11/1

N2 - 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 (SCCD-set) 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 Gallai-type 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.

AB - 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 (SCCD-set) 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 Gallai-type 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.

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M3 - Article

AN - SCOPUS:85177062025

SN - 1816-093X

VL - 31

SP - 1480

EP - 1485

JO - Engineering Letters

JF - Engineering Letters

IS - 4

ER -

Strong (Weak) Full cc-domination in a Graph

Abstract

All Science Journal Classification (ASJC) codes

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