简单图的支配数和上可嵌入性(英文)  

Domination number and upper embeddability of a simple graph

作　　者：王涛[1] 李德明[2] 

机构地区：[1]华北科技学院基础部,河北三河065201 [2]首都师范大学数学系,北京100048

出　　处：《安徽大学学报（自然科学版）》2012年第6期11-15,共5页Journal of Anhui University(Natural Science Edition)

基　　金：Supported by National Natural Science Foundation of China(10201022,10971144);the Natural Science Foundation of Beijing City(1102015);the Fundamental Research Funds for the Central Universities(2011B019)

摘　　要：设图G是n阶简单连通图.如果G的支配数为1,则G是上可嵌入的.如果G是2-边连通且G的支配数为2,则G是上可嵌入的.如果G是3-边连通且G的支配数为3,则G的最大亏格介于|(β(G)-2)/2|和|β(G)/2|之间,其中β(G)=|E(G)|-|V(G)|+1.论文得到了一些在控制数和边连通度条件下的最大亏格的界.Let G be a connected simple graph of order n. If the domination number of G was 1, G was upper embeddable. If G was 2-edge connected, and the domination number of G was 2, G was upper embeddable. If G was 3-edge connected, and the domination number of G was 3, the maximum genus of G was ｜（β（G） -2）/2｜ ≤g_M（G） ≤ ｜β（ G）/2｜, whereβ（G） = ｜E（G） ｜-｜ V（G） ｜＋1. And we got some other results on the bound of the maximum genus of a graph with constraints of domination number and edge connectivity.

关 键 词：支配数 最大亏格 上可嵌入性 顶点度和 亏格 

分 类 号：O175.5[理学—数学]