ON CLIQUE-CLIQUE DOMINATION NUMBER AND INVERSE CLIQUE TRANSVERSAL NUMBER OF A GRAPH

Surekha R. Bhat; R. S. Bhat; Smitha Ganesh Bhat

doi:10.17777/pjms2024.27.4.733

ON CLIQUE-CLIQUE DOMINATION NUMBER AND INVERSE CLIQUE TRANSVERSAL NUMBER OF A GRAPH

Surekha R. Bhat^*
, R. S. Bhat^*
, Smitha Ganesh Bhat^*

^*Corresponding author for this work

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

Abstract

Let K(G) denote set of all cliques of a graph G. Two cliques l₁, l₂ ∈ K(G) are said to clique dominate each other if there is a vertex common to both l₁ and l₂. A set [Formula presented] is said to be a clique-clique dominating set (CCD-set) if every clique in G is clique dominated by some clique in L. The clique-clique dominating set having minimum cardinality is called clique-clique domination number [Formula presented]. In this paper, several bounds for the above parameter are obtained. Also bounds on number of cliques in a graph is given in terms of clique numbers.

Original language	English
Pages (from-to)	733-742
Number of pages	10
Journal	Proceedings of the Jangjeon Mathematical Society
Volume	27
Issue number	4
DOIs	https://doi.org/10.17777/pjms2024.27.4.733
Publication status	Published - 2024

All Science Journal Classification (ASJC) codes

General Mathematics

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10.17777/pjms2024.27.4.733

Cite this

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title = "ON CLIQUE-CLIQUE DOMINATION NUMBER AND INVERSE CLIQUE TRANSVERSAL NUMBER OF A GRAPH",

abstract = "Let K(G) denote set of all cliques of a graph G. Two cliques l1, l2 ∈ K(G) are said to clique dominate each other if there is a vertex common to both l1 and l2. A set [Formula presented] is said to be a clique-clique dominating set (CCD-set) if every clique in G is clique dominated by some clique in L. The clique-clique dominating set having minimum cardinality is called clique-clique domination number [Formula presented]. In this paper, several bounds for the above parameter are obtained. Also bounds on number of cliques in a graph is given in terms of clique numbers.",

author = "Bhat, \{Surekha R.\} and Bhat, \{R. S.\} and Bhat, \{Smitha Ganesh\}",

year = "2024",

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pages = "733--742",

journal = "Proceedings of the Jangjeon Mathematical Society",

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AU - Bhat, R. S.

AU - Bhat, Smitha Ganesh

PY - 2024

Y1 - 2024

N2 - Let K(G) denote set of all cliques of a graph G. Two cliques l1, l2 ∈ K(G) are said to clique dominate each other if there is a vertex common to both l1 and l2. A set [Formula presented] is said to be a clique-clique dominating set (CCD-set) if every clique in G is clique dominated by some clique in L. The clique-clique dominating set having minimum cardinality is called clique-clique domination number [Formula presented]. In this paper, several bounds for the above parameter are obtained. Also bounds on number of cliques in a graph is given in terms of clique numbers.

AB - Let K(G) denote set of all cliques of a graph G. Two cliques l1, l2 ∈ K(G) are said to clique dominate each other if there is a vertex common to both l1 and l2. A set [Formula presented] is said to be a clique-clique dominating set (CCD-set) if every clique in G is clique dominated by some clique in L. The clique-clique dominating set having minimum cardinality is called clique-clique domination number [Formula presented]. In this paper, several bounds for the above parameter are obtained. Also bounds on number of cliques in a graph is given in terms of clique numbers.

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ER -

ON CLIQUE-CLIQUE DOMINATION NUMBER AND INVERSE CLIQUE TRANSVERSAL NUMBER OF A GRAPH

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