Clique Free Number of a Graph

Surekha Ravishankar Bhat; Ravishankar Bhat; Smitha Ganesh Bhat

Clique Free Number of a Graph

Surekha Ravishankar Bhat
, Ravishankar Bhat
, Smitha Ganesh Bhat^*

^*Corresponding author for this work

Manipal Institute of Technology, Manipal

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

3 Citations (Scopus)

Abstract

A complete maximal subgraph of a graph H is designated as a clique. A set (Math Presents) is clique free if <S>, the subgraph induced by the set S does not induce any clique of H. The clique free number β_vc = β_vc(H) is the maximum order of a clique free set of H. In this present work, we have deduced few bounds for cilque free number and have substantiated the graphs attaining the same. Also, a Gallai’s theorem type result for clique free number is proved and Konig-Egervarey Theorem is extended to clique free sets. An algorithm to find all the maximal clique free sets is derived.

Original language	English
Pages (from-to)	1832-1836
Number of pages	5
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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abstract = "A complete maximal subgraph of a graph H is designated as a clique. A set (Math Presents) is clique free if , the subgraph induced by the set S does not induce any clique of H. The clique free number βvc = βvc(H) is the maximum order of a clique free set of H. In this present work, we have deduced few bounds for cilque free number and have substantiated the graphs attaining the same. Also, a Gallai{\textquoteright}s theorem type result for clique free number is proved and Konig-Egervarey Theorem is extended to clique free sets. An algorithm to find all the maximal clique free sets is derived.",

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AU - Bhat, Smitha Ganesh

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N2 - A complete maximal subgraph of a graph H is designated as a clique. A set (Math Presents) is clique free if , the subgraph induced by the set S does not induce any clique of H. The clique free number βvc = βvc(H) is the maximum order of a clique free set of H. In this present work, we have deduced few bounds for cilque free number and have substantiated the graphs attaining the same. Also, a Gallai’s theorem type result for clique free number is proved and Konig-Egervarey Theorem is extended to clique free sets. An algorithm to find all the maximal clique free sets is derived.

AB - A complete maximal subgraph of a graph H is designated as a clique. A set (Math Presents) is clique free if , the subgraph induced by the set S does not induce any clique of H. The clique free number βvc = βvc(H) is the maximum order of a clique free set of H. In this present work, we have deduced few bounds for cilque free number and have substantiated the graphs attaining the same. Also, a Gallai’s theorem type result for clique free number is proved and Konig-Egervarey Theorem is extended to clique free sets. An algorithm to find all the maximal clique free sets is derived.

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JO - Engineering Letters

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ER -

Clique Free Number of a Graph

Abstract

All Science Journal Classification (ASJC) codes

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