Edge domination in graphs
type: Item
instance of: scholarly article
title: Edge domination in graphs
zbMATH Open document ID: 0906.05032
author: S. Arumugam
author: S. Velammal
published in: Taiwanese Journal of Mathematics
publication date: 1998-07-28T00:00:00Z
review text: An edge dominating set in a graph \(G\) is a subset \(X\) of the edge set \(E(G)\) of \(G\) such that each edge of \(G\) either is in \(X\), or has a common end vertex with an edge of \(X\). The edge domination number \(\gamma'(G)\) of \(G\) is the minimum number of edges of an edge dominating set in \(G\). The maximum number of classes of a partition of \(E(G)\) into edge dominating sets is the edge domatic number \(d'(G)\) of \(G\). The paper characterizes graphs \(G\) for which \(\gamma'(G)= p/2\) and graphs \(G\) for which \(\gamma'(G)+ d'(G)= q+1\), where \(p\) is the number of vertices and \(q\) is the number of edges of \(G\). Further, trees and unicyclic graphs with \(\gamma'(G)= \lfloor p/2\rfloor\) and \(\gamma'(G)= q-\Delta'\) are characterized, where \(\Delta'\) is the maximum degree of an edge of \(G\).
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 1179918
zbMATH Keywords: edge dominating set
zbMATH Keywords: edge domination number
zbMATH Keywords: edge domatic number
reviewed by: Bohdan Zelinka
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500406930
OpenAlex ID: W4254993802
DOI: 10.11650/TWJM/1500406930
description: scientific article; zbMATH DE number 1179918