2-控制数和连通2-控制数相等的图(英文)  

On Graphs with Equal 2-domination and Connected 2-domination Numbers

作　　者：焦艳[1] 于洪全[1] 

机构地区：[1]大连理工大学应用数学系,辽宁大连116024

出　　处：《应用数学》2004年第S1期88-92,共5页Mathematica Applicata

摘　　要：任意一个图G =(V ,E) ,S是V(G)的子集 ,如果对每一个顶点u∈V-S都存在顶点v∈S ,使得d(u ,v) ≤ 2 ,则称S为G的一个 2 控制 .称最小的 2 控制集的顶点个数为G的 2 控制数 ,记为γ2 (G) .如果G的一个 2 控制集S的生成子集〈S〉是一个连通图 ,则称S为G的一个连通 2 控制集 .称最小的连通 2 控制集的顶点个数为G的连通 2 控制数 ,记为γc2 (G) .本文论述了树和单圈图中 2 控制数和连通 2 控制数相等的充分必要条件 .For a graph G=(V,E),a subset SV(G) is said to be a 2-dominating set of G if for each vertex u∈V-S,there exists a vertex v∈S such that d(u,v)≤2.The minimum cardinality of 2-dominating sets of G is called the 2-domination number of G and denoted by γ 2(G).A 2-dominating set S is called a connected 2-dominating set of G,if the induced subgraph 〈S〉 is connected,the connected 2-domination number of G,denoted by γc 2(G),is the minimum cardinality of connected 2-dominating sets of G.In this paper,we characterize the class of trees and unicyclic graphs for which the 2-domination numbers are equal to the connected 2-domination numbers.

关 键 词：2-控制数 连通2-控制数 单圈图 

分 类 号：O157.5[理学—数学]