Distance-balanced graphs

被引：72
|
作者：
Jerebic, Janja [1 ]
Klavzar, Sandi [1 ]
Rall, Douglas F. [2 ]
机构：
[1] Univ Maribor, Dept Math & Comp Sci, FNM, SLO-2000 Maribor, Slovenia
[2] Furman Univ, Dept Math, Greenville, SC 29613 USA
来源：
ANNALS OF COMBINATORICS | 2008年 / 12卷 / 01期
关键词：
graph distance; distance-balanced graphs; graph products; connectivity;
D O I：
10.1007/s00026-008-0337-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: The number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. The new concept is connected with symmetry conditions in graphs and local operations on graphs are studied with respect to it. Distance-balanced Cartesian and lexicographic products of graphs are also characterized. Several open problems are posed along the way.
引用
收藏
页码：71 / 79
页数：9
相关论文
共 50 条
  • [11] Distance-balanced graphs: Symmetry conditions
    Kutnar, Klavdija
    Malnic, Aleksander
    Marusic, Dragan
    Miklavic, Stefko
    DISCRETE MATHEMATICS, 2006, 306 (16) : 1881 - 1894
  • [12] FURTHER RESULTS ON DISTANCE-BALANCED GRAPHS
    Tavakoli, M.
    Rahbarnia, F.
    Ashrafi, A. R.
    UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2013, 75 (01): : 77 - 84
  • [13] On the connectivity of bipartite distance-balanced graphs
    Miklavic, Stefko
    Sparl, Primoz
    EUROPEAN JOURNAL OF COMBINATORICS, 2012, 33 (02) : 237 - 247
  • [14] Quasi-λ-distance-balanced graphs
    Abedi, Amirabbas
    Alaeiyan, Mehdi
    Hujdurovic, Ademir
    Kutnar, Klavdija
    DISCRETE APPLIED MATHEMATICS, 2017, 227 : 21 - 28
  • [15] ON THE NEW EXTENSION OF DISTANCE-BALANCED GRAPHS
    Faghani, Morteza
    Pourhadi, Ehsan
    Kharazi, Hassan
    TRANSACTIONS ON COMBINATORICS, 2016, 5 (04) : 21 - 34
  • [16] On certain regular nicely distance-balanced graphs
    Fernández, Blas
    Miklavič, Štefko
    Penjić, Safet
    arXiv, 2021,
  • [17] Distance-balanced graphs and travelling salesman problems
    Cavaleri, Matteo
    Donno, Alfredo
    ARS MATHEMATICA CONTEMPORANEA, 2020, 19 (02) : 311 - 324
  • [18] On some problems regarding distance-balanced graphs
    Fernandez, Blas
    Hujdurovic, Ademir
    EUROPEAN JOURNAL OF COMBINATORICS, 2022, 106
  • [19] ON CERTAIN REGULAR NICELY DISTANCE-BALANCED GRAPHS
    Fernandez, Blas
    Miklavic, Stefko
    Penjic, Safet
    REVISTA DE LA UNION MATEMATICA ARGENTINA, 2023, 65 (01): : 165 - 185
  • [20] Strongly distance-balanced graphs and graph products
    Balakrishnan, Kannan
    Changat, Manoj
    Peterin, Iztok
    Spacapan, Simon
    Sparl, Primoz
    Subhamathi, Ajitha R.
    EUROPEAN JOURNAL OF COMBINATORICS, 2009, 30 (05) : 1048 - 1053
12345