On ve-degrees and ev-degrees in graphs

Let G=(V,E) be a graph with vertex set V and edge set E. A vertex v∈Vve-dominates every edge incident to it as well as every edge adjacent to these incident edges. The vertex–edge degree of a vertex v is the number of edges ve-dominated by v. Similarly, an edge e=uv ev-dominates the two vertices u a...

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Bibliographic Details
Published inDiscrete mathematics Vol. 340; no. 2; pp. 31 - 38
Main Authors Chellali, Mustapha, Haynes, Teresa W., Hedetniemi, Stephen T., Lewis, Thomas M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 06.02.2017
Subjects
Degree
Edge–vertex degree
Edge–vertex domination
Irregular graph
Regular graph
Vertex
Vertex–edge degree
Vertex–edge domination
Vertex
Edge–vertex domination
Vertex–edge degree
Degree
Edge–vertex degree
Irregular graph
Regular graph
Vertex–edge domination
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Summary:Let G=(V,E) be a graph with vertex set V and edge set E. A vertex v∈Vve-dominates every edge incident to it as well as every edge adjacent to these incident edges. The vertex–edge degree of a vertex v is the number of edges ve-dominated by v. Similarly, an edge e=uv ev-dominates the two vertices u and v incident to it, as well as every vertex adjacent to u or v. The edge–vertex degree of an edge e is the number of vertices ev-dominated by edge e. In this paper we introduce these types of degrees and study their properties.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2016.07.008