On Connected Partial Domination in Graphs

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i4.4168

Keywords:

Partial domination, Connected Partial domination, Join, Corona, Lexicographic product, Cartesian product

Abstract

This paper introduces and investigates a variant of partial domination called the connected α-partial domination. For any graph G = (V (G), E(G)) and α ∈ (0, 1], a set S ⊆ V (G) is an α-partial dominating set in G if |N[S]| ≥ α |V (G)|. An α-partial dominating set S ⊆ V (G) is a connected α-partial dominating set in G if ⟨S⟩, the subgraph induced by S, is connected. The connected α-partial domination number of G, denoted by ∂Cα(G), is the smallest cardinality of a connected α-partial dominating set in G. In this paper, we characterize the connected α-partial dominating sets in the join and lexicographic product of graphs for any α ∈ (0, 1] and determine the corresponding connected α-partial domination numbers of graphs resulting from the said binary operations. Moreover, we establish sharp bounds for the connected α-partial domination numbers of the corona and Cartesian product of graphs. Furthermore, we determine ∂Cα(G) of some special graphs when α =1/2. Several realization problems are also generated in this paper.

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How to Cite

Cabulao, J. M. C., & Isla, R. T. (2021). On Connected Partial Domination in Graphs. European Journal of Pure and Applied Mathematics, 14(4), 1490–1506. https://doi.org/10.29020/nybg.ejpam.v14i4.4168