Transversal Hop Domination in Graphs

Author:

Bonsocan Maria Andrea,Jamil Ferdinand

Abstract

Let G be a graph. A set S ⊆ V (G) is a hop dominating set of G if for every v ∈ V (G)\S, there exists u ∈ S such that dG(u, v) = 2. The minimum cardinality γh(G) of a hop dominating set is the hop domination number of G. Any hop dominating set of G of cardinality γh(G) is a γh-set of G. A hop dominating set S of G which intersects every γh-set of G is a transversal hop dominating set. The minimum cardinality γbh(G) of a transversal hop dominating set in G is the transversal hop domination number of G. In this paper, we initiate the study of transversal hop domination. First, we characterize graphs G whose values for γbh(G) are either n or n − 1, and we determine the specific values of γbh(G) for some specific graphs. Next, we show that for every positive integers a and b with a ≥ 2 and b ≥ 3a, there exists a connected graph G on b vertices such that γbh(G) = a. We also show that for every positive integers a and b with 2 ≤ a ≤ b, there exists a connected graph G for which γh(G) = a and γbh(G) = b. Finally, we investigate the transversal hop dominating sets in the join and corona of two graphs, and determine their corresponding transversal hop domination numbers.

Funder

Department of Science and Technology, Philippines

Publisher

New York Business Global LLC

Subject

Applied Mathematics,Geometry and Topology,Numerical Analysis,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Closed Geodetic Hop Domination in Graphs;European Journal of Pure and Applied Mathematics;2024-07-31

2. Transversal total hop domination in graphs;Discrete Mathematics, Algorithms and Applications;2023-12-22

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