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
  • [21] A note on the distance-balanced property of generalized Petersen graphs
    Yang, Rui
    Hou, Xinmin
    Li, Ning
    Zhong, Wei
    ELECTRONIC JOURNAL OF COMBINATORICS, 2009, 16 (01):
  • [22] SOME RESULTS ON DISTANCED-BALANCED AND STRONGLY DISTANCE-BALANCED GRAPHS
    Faramarzi, H.
    Rahbarnia, F.
    Tavakoli, M.
    ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2018, (40): : 98 - 107
  • [23] The strongly distance-balanced property of the generalized Petersen graphs
    Kutnar, Klavdija
    Malnic, Aleksander
    Marusic, Dragan
    Miklavic, Stefko
    ARS MATHEMATICA CONTEMPORANEA, 2009, 2 (01) : 41 - 47
  • [24] Equal opportunity networks, distance-balanced graphs, and Wiener game
    Balakrishnan, Kannan
    Bresar, Bostjan
    Changat, Manoj
    Klavzar, Sandi
    Vesel, Aleksander
    Pletersek, Petra Zigert
    DISCRETE OPTIMIZATION, 2014, 12 : 150 - 154
  • [25] The complexity of obtaining a distance-balanced graph
    Cabello, Sergio
    Luksic, Primoz
    ELECTRONIC JOURNAL OF COMBINATORICS, 2011, 18 (01):
  • [26] Status connectivity indices and co-indices of graphs and its computation to some distance-balanced graphs
    Ramane, Harishchandra S.
    Yalnaik, Ashwini S.
    Sharafdini, Reza
    AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS, 2020, 17 (01) : 98 - 108
  • [27] Local testability of distance-balanced quantum codes
    Wills, Adam
    Lin, Ting-Chun
    Hsieh, Min-Hsiu
    NPJ QUANTUM INFORMATION, 2024, 10 (01)
  • [28] l-distance-balanced graphs
    Miklavic, Stefko
    Sparl, Primoz
    DISCRETE APPLIED MATHEMATICS, 2018, 244 : 143 - 154
  • [29] On 2-distance-balanced graphs
    Frelih, Bostjan
    Miklavic, Stefko
    ARS MATHEMATICA CONTEMPORANEA, 2018, 15 (01) : 81 - 95
  • [30] On l-Distance-Balanced Product Graphs
    Jerebic, Janja
    Klavzar, Sandi
    Rus, Gregor
    GRAPHS AND COMBINATORICS, 2021, 37 (01) : 369 - 379
12345