ON THE PARTITION DIMENSION OF INFINITE GRAPHS

被引：0
作者：
Imran, Muhammad [1 ]
Vetrik, Tomas [2 ]
机构：
[1] United Arab Emirates Univ, Dept Math Sci, Coll Sci, Al Ain, U Arab Emirates
[2] Univ Free State, Dept Math & Appl Math, Bloemfontein, South Africa
来源：
MATHEMATICAL REPORTS | 2022年 / 24卷 / 03期
基金：
新加坡国家研究基金会;
关键词：
partition dimension; infinite graph; distance; METRIC DIMENSION;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Little is known about the partition dimension of infinite graphs. Tomescu studied graphs where the set of vertices is the set of points of the integer lattice. We generalize these graphs and present several exact values, lower bounds and upper bounds on the partition dimension of infinite graphs.
引用
收藏
页码：433 / 442
页数：10
相关论文
共 14 条
  • [1] On the star partition dimension of comb product of cycle and complete graph
    Alfarisi, Ridho
    Darmaji
    Dafik
    [J]. INTERNATIONAL CONFERENCE ON MATHEMATICS: EDUCATION, THEORY AND APPLICATION, 2017, 855
  • [2] Baskoro ET, 2012, FAR E J MATH SCI, V66, P181
  • [3] On the metric dimension of infinite graphs
    Caceres, J.
    Hernando, C.
    Mora, M.
    Pelayo, I. M.
    Puertas, M. L.
    [J]. DISCRETE APPLIED MATHEMATICS, 2012, 160 (18) : 2618 - 2626
  • [4] Chartrand E., 2000, Aequa-tiones Math., V59, P45, DOI [10.1007/PL00000127, DOI 10.1007/PL00000127]
  • [5] Resolvability in graphs and the metric dimension of a graph
    Chartrand, G
    Eroh, L
    Johnson, MA
    Oellermann, OR
    [J]. DISCRETE APPLIED MATHEMATICS, 2000, 105 (1-3) : 99 - 113
  • [6] The partition dimension of strong product graphs and Cartesian product graphs
    Gonzalez Yero, Ismael
    Jakovac, Marko
    Kuziak, Dorota
    Taranenko, Andrej
    [J]. DISCRETE MATHEMATICS, 2014, 331 : 43 - 52
  • [7] Harary F., 1976, ARS COMBINATORIA, V2, P191
  • [8] On the partition dimension of two-component graphs
    Haryeni, D. O.
    Baskoro, E. T.
    Saputro, S. W.
    Baca, M.
    Semanicova-Fenovcikova, A.
    [J]. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2017, 127 (05): : 755 - 767
  • [9] Landmarks in graphs
    Khuller, S
    Raghavachari, B
    Rosenfeld, A
    [J]. DISCRETE APPLIED MATHEMATICS, 1996, 70 (03) : 217 - 229
  • [10] METRIC BASES IN DIGITAL GEOMETRY
    MELTER, RA
    TOMESCU, I
    [J]. COMPUTER VISION GRAPHICS AND IMAGE PROCESSING, 1984, 25 (01): : 113 - 121
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