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
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