On Idomatic Partitions of Direct Products of Complete Graphs

被引：0
|
作者：
Sandi Klavžar
Gašper Mekiš
机构：
[1] University of Ljubljana,Faculty of Mathematics and Physics
[2] University of Maribor,Faculty of Natural Sciences and Mathematics
[3] Institute of Mathematics,undefined
[4] Physics and Mechanics,undefined
来源：
Graphs and Combinatorics | 2011年 / 27卷
关键词：
Independent set; Dominating set; Idomatic partition; Direct product of graph; Complete graph;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Independent dominating sets in the direct product of four complete graphs are considered. Possible types of such sets are classified. The sets in which every pair of vertices agree in exactly one coordinate, called T1-sets, are explicitly described. It is proved that the direct product of four complete graphs admits an idomatic partition into T1-sets if and only if each factor has at least three vertices and the orders of at least two factors are divisible by 3.
引用
收藏
页码：713 / 726
页数：13
相关论文
共 50 条
  • [1] On Idomatic Partitions of Direct Products of Complete Graphs
    Klavzar, Sandi
    Mekis, Gasper
    [J]. GRAPHS AND COMBINATORICS, 2011, 27 (05) : 713 - 726
  • [2] Idomatic partitions of direct products of complete graphs
    Valencia-Pabon, Mario
    [J]. DISCRETE MATHEMATICS, 2010, 310 (05) : 1118 - 1122
  • [3] Complete partitions of graphs
    Magnús M. Halldórsson
    Guy Kortsarz
    Jaikumar Radhakrishnan
    Sivaramakrishnan Sivasubramanian
    [J]. Combinatorica, 2007, 27
  • [4] Complete partitions of graphs
    Halldorsson, Magnus M.
    Kortsarz, Guy
    Radhakrishnan, Jaikumar
    Sivasubramanian, Sivaramakrishnan
    [J]. COMBINATORICA, 2007, 27 (05) : 519 - 550
  • [5] Complete Partitions of Graphs
    Kortsarz, Guy
    Radhakrishnan, Jaikumar
    Sivasubramanian, Sivaramakrishnan
    [J]. PROCEEDINGS OF THE SIXTEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2005, : 860 - 869
  • [6] Domination in direct products of complete graphs
    Vemuri, Harish
    [J]. DISCRETE APPLIED MATHEMATICS, 2020, 285 : 473 - 482
  • [7] Equitable chromatic threshold of direct products of complete graphs
    Yan, Zhidan
    Wang, Wei
    [J]. ARS COMBINATORIA, 2014, 114 : 235 - 243
  • [8] Minimum cycle bases of direct products of complete graphs
    Hammack, Richard
    [J]. INFORMATION PROCESSING LETTERS, 2007, 102 (05) : 214 - 218
  • [9] Distinguishing partitions of complete multipartite graphs
    Goff, Michael
    [J]. ARS MATHEMATICA CONTEMPORANEA, 2016, 10 (01) : 45 - 66
  • [10] DISTANCE THREE LABELINGS FOR DIRECT PRODUCTS OF THREE COMPLETE GRAPHS
    Kim, Byeong Moon
    Song, Byung Chul
    Hwang, Woonjae
    [J]. TAIWANESE JOURNAL OF MATHEMATICS, 2013, 17 (01): : 207 - 219
12345