Transversal Hop Domination in Graphs
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Published:2023-01-29
Issue:1
Volume:16
Page:192-206
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ISSN:1307-5543
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Container-title:European Journal of Pure and Applied Mathematics
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language:
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Short-container-title:Eur. J. Pure Appl. Math.
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.
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