Graphs with unique minimum edge-vertex dominating sets

被引：0
|
作者：
Senthilkumar, B. [1 ]
Chellali, M. [1 ,2 ]
Kumar, H. Naresh [1 ]
Venkatakrishnan, Y. B. [1 ]
机构：
[1] SASTRA Deemed Univ, Dept Math, Tanjore, Tamil Nadu, India
[2] Univ Blida, Dept Math, LAMDA RO Lab, BP 270, Blida, Algeria
来源：
COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION | 2025年 / 10卷 / 01期
关键词：
Edge-vertex dominating set; edge-vertex domination number; trees; TREES; NUMBER;
D O I：
10.22049/cco.2023.28605.1631
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An edge e of a simple graph G = (VG, EG) is said to ev-dominate a vertex v & ISIN; VG if e is incident with v or e is incident with a vertex adjacent to v. A subset D & SUBE; EG 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.
引用
收藏
页码：99 / 109
页数：11
相关论文
共 50 条
  • [31] Convex grid drawings of planar graphs with constant edge-vertex resolution
    Bekos, Michael A.
    Gronemann, Martin
    Montecchiani, Fabrizio
    Symvonis, Antonios
    THEORETICAL COMPUTER SCIENCE, 2024, 982
  • [32] A note on the minimum edge dominating energy of graphs
    Mohammad Hadi Akhbari
    Kok Keong Choong
    Fateme Movahedi
    Journal of Applied Mathematics and Computing, 2020, 63 : 295 - 310
  • [33] A note on the minimum edge dominating energy of graphs
    Akhbari, Mohammad Hadi
    Choong, Kok Keong
    Movahedi, Fateme
    JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2020, 63 (1-2) : 295 - 310
  • [34] Convex Grid Drawings of Planar Graphs with Constant Edge-Vertex Resolution
    Bekos, Michael A.
    Gronemann, Martin
    Montecchiani, Fabrizio
    Symvonis, Antonios
    COMBINATORIAL ALGORITHMS (IWOCA 2022), 2022, 13270 : 157 - 171
  • [35] Total edge-vertex domination
    Sahin, Abdulgani
    Sahin, Bunyamin
    RAIRO-THEORETICAL INFORMATICS AND APPLICATIONS, 2020, 54
  • [36] On minimum intersection of two minimum dominating sets of interval graphs
    Chang, MS
    Hsu, CC
    DISCRETE APPLIED MATHEMATICS, 1997, 78 (1-3) : 41 - 50
  • [37] Edge Geodetic Dominating Sets of Some Graphs
    Quije, Clint Joy M.
    Mariano, Rochelleo E.
    Ahmad, Eman C.
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2025, 18 (01):
  • [38] Trees with unique minimum p-dominating sets
    Lu, You
    Hou, Xinmin
    Xu, Jun-Ming
    Li, Ning
    UTILITAS MATHEMATICA, 2011, 86 : 193 - 205
  • [39] A characterization of trees with unique minimum double dominating sets
    Chellali, Mustapha
    Haynes, Teresa W.
    UTILITAS MATHEMATICA, 2010, 83 : 233 - 242
  • [40] Graphs with unique minimum paired-dominating set
    Chen, Lei
    Lu, Changhong
    Zeng, Zhenbing
    ARS COMBINATORIA, 2015, 119 : 177 - 192
12345