On γ-free, γ-totally-free and γ-fixed sets in graphs

Document Type : Original paper

Authors

1 Department of Mathematics, S. D. College, Alappuzha-690 104, India

2 Department of Studies in Mathematics, University of Mysore, Manasagangothri, Mysuru-570 006, India

3 Adjunct Professor, Department of Computer Science and Engineering, Ramco Institute of Technology, Rajapalayam-626 117, Tamil Nadu, India

Abstract

Let G=(V,E) be a connected graph. A subset S of V is called a γ-free set if there exists a γ-set D of G such that S∩D=∅. If further the induced subgraph H=G[V−S] is connected, then S is called a  cc-γ-free set of G. We use this concept to identify connected induced subgraphs H of a given graph G such that γ(H)≤γ(G). We also introduce the concept of γ-totally-free and γ-fixed sets and present several basic results on the corresponding parameters. 

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References

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Communications in Combinatorics and Optimization
Volume 9, Issue 4
December 2024
Pages 647-654

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