The p-Bondage Number of Trees

被引：4

作者：

Lu, You ^{[2
]}

Xu, Jun-Ming ^{[1
]}

机构：

[1] Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China

[2] NW Polytech Univ, Dept Appl Math, Xian 710072, Shaanxi, Peoples R China

来源：

GRAPHS AND COMBINATORICS | 2011年 / 27卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Domination; Bondage number; p-Domination; p-Bondage number; Trees; EXTENDED DE-BRUIJN; DOMINATION NUMBER; KAUTZ DIGRAPHS; PLANAR GRAPHS; BOUNDS;

D O I：

10.1007/s00373-010-0956-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p be a positive integer and G =( V, E) be a simple graph. A p- dominating set of G is a subset D subset of V such that every vertex not in D has at least p neighbors in D. The p-domination number of G is the minimum cardinality of a p-dominating set of G. The p-bondage number of a graph G with Delta(G) >= p is the minimum cardinality among all sets of edges B subset of E for which gamma p(G - B) > gamma(G). For any integer p >= 2 and tree T with Delta(T) >= p, this paper shows that 1 <= b(p)(T) <= (T) - p + 1, and characterizes all trees achieving the equalities.

引用

页码：129 / 141

页数：13

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