On Connected Co-Independent Hop Domination in Graphs

Authors

  • Sandra Abo Nanding Mindanao State University-Iligan Institute of Technology
  • Helen Rara Center of Graph Theory, Algebra, and Analysis-Premier Research Institute of Science and Mathematics, Mindanao State University-Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i4.4069

Keywords:

connected co-independent hop dominating set, connected co-independent hop domination number, strictly co-independent set, strictly co-independent number, join, corona, lexicographic product

Abstract

Let G be a connected graph. A subset S of V (G) is a connected co-independent hop dominating set in G if the subgraph induced by S is connected and V (G)\S is an independent set where for each v ∈ V (G)\S, there exists a vertex u ∈ S such that dG(u, v) = 2. The smallest cardinality of such an S is called the connected co-independent hop domination number of G. This paper presents the characterizations of the connected co-independent hop dominating sets in the join, corona and lexicographic product of two graphs. It also discusses the corresponding connected co-independent hop domination numbers of the aforementioned graphs.

Author Biography

Helen Rara, Center of Graph Theory, Algebra, and Analysis-Premier Research Institute of Science and Mathematics, Mindanao State University-Iligan Institute of Technology

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How to Cite

Nanding, S. A., & Rara, H. (2021). On Connected Co-Independent Hop Domination in Graphs. European Journal of Pure and Applied Mathematics, 14(4), 1226–1236. https://doi.org/10.29020/nybg.ejpam.v14i4.4069

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