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Graphs with unique minimum edge-vertex dominating sets | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 6، دوره 10، شماره 1، خرداد 2025، صفحه 99-109 اصل مقاله (377.28 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28605.1631 | ||
| نویسندگان | ||
| B. Senthilkumar1؛ M. Chellali2؛ H. Naresh Kumar1؛ V. B. Yanamandram* 1 | ||
| 1Department of Mathematics, SASTRA Deemed to be University, Thanjavur, Tamil Nadu, India | ||
| 2LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria | ||
| چکیده | ||
| An edge $e$ of a simple graph $G=(V_{G},E_{G})$ is said to ev-dominate a vertex $v\in V_{G}$ if $e$ is incident with $v$ or $e$ is incident with a vertex adjacent to $v$. A subset $D\subseteq E_{G}$ is an edge-vertex dominating set (or an evd-set for short) of $G$ if every vertex of $G$ is ev-dominated by an edge of $D$. The edge-vertex domination number of $G$ is the minimum cardinality of an evd-set of $G$. In this paper, we initiate the study of the graphs with unique minimum evd-sets that we will call UEVD-graphs. We first present some basic properties of UEVD-graphs, and then we characterize UEVD-trees by equivalent conditions as well as by a constructive method. | ||
| کلیدواژهها | ||
| edge-vertex domination؛ edge-vertex domination number؛ trees | ||
| مراجع | ||
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