Volume 57, Number 4, July-August 2023
|Page(s)||1785 - 1795|
|Published online||14 July 2023|
Graphs with unique minimum vertex-edge dominating sets
Department of Mathematics, SASTRA Deemed University, Tanjore, Tamilnadu, India
2 LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270 Blida, Algeria
* Corresponding author: email@example.com
Accepted: 30 May 2023
A vertex u of a graph G = (V, E), ve-dominates every edge incident to u, as well as every edge adjacent to these incident edges. A set S ⊆ V is a vertex-edge dominating set (or a ved-set for short) if every edge of E is ve-dominated by at least one vertex of S. The vertex-edge domination number is the minimum cardinality of a ved-set in G. In this paper, we investigate the graphs having unique minimum ved-sets that we will call UVED-graphs. We start by giving some basic properties of UVED-graphs. For the class of trees, we establish two equivalent conditions characterizing UVED-trees which we subsequently complete by providing a constructive characterization.
Mathematics Subject Classification: 05C69
Key words: Vertex-edge domination / Vertex-edge domination number / Trees
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.