Double Edge–Vertex Domination

Şahin, Bünyamin; Şahi̇n, Abdulgani̇

doi:10.1007/978-3-030-51156-2_182

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2021

2023

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Cited by 2 publications

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“…They gave a linear time algorithm to find in proper interval graphs and also showed that finding in general graphs with vertices having degree at most 5 is APX-complete. The double version of edge-vertex domination was studied by Sahin and Sahin [12]. They also gave the relationship between and , , for trees and graphs, and also gave formulas to determine the double ev-domination number of paths and cycles.…”

Section: Related Workmentioning

confidence: 99%

Edge-Vertex Dominating Set in Unit Disk Graphs

Singireddy¹,

Basappa²

2021

Preprint

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Given an undirected graph = ( , ), a vertex ∈ is edge-vertex (ev) dominated by an edge ∈ if is either incident to or incident to an adjacent edge of . A set ⊆ is an edgevertex dominating set (referred to as ev-dominating set) of if every vertex of is ev-dominated by at least one edge of . The minimum cardinality of an ev-dominating set is the ev-domination number. The edge-vertex dominating set problem is to find a minimum ev-domination number. In this paper we prove that the ev-dominating set problem is NP-hard on unit disk graphs. We also prove that this problem admits a polynomial-time approximation scheme on unit disk graphs. Finally, we give a simple 5-factor linear-time approximation algorithm.

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Section: Related Workmentioning

confidence: 99%