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Graphs with unique minimum edge-vertex dominating sets | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 شهریور 1402 اصل مقاله (376.34 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28605.1631 | ||
| نویسندگان | ||
| B Senthilkumar1؛ M Chellali2؛ Naresh Kumar H1؛ Venkatakrishnan 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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[11] Y.B. Venkatakrishnan and B. Krishnakumari, An improved upper bound of edge–vertex domination number of a tree, Information Processing Letters 134 (2018), 14–17. https://doi.org/10.1016/j.ipl.2018.01.012 [12] W. Zhao, F. Wang, and H. Zhang, Construction for trees with unique minimum dominating sets, Int. J. Comput. Math. Comput. Sys. Theory 3 (2018), no. 3, 204–213. https://doi.org/10.1080/23799927.2018.1531930 | ||
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