The copnumber for lexicographic products and sums of graphs

Contributions to Discrete Mathematics

Bernd Schroeder¹ 

[1] Louisiana Tech University

关键词: discrete mathematics;    graph;    cops and robber;    retraction;    dismantlable;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: University of Calgary * Department of Mathematics and Statistics

【 摘 要 】

For the lexicographic product$G\bullet H$of two graphs$G$and$H$so that$G$is connected, we prove that if thecopnumber $c(G)$of$G$is greater than or equal to$2$ , then$c(G\bullet H)=c(G)$ . Moreover, if$c(G)=c(H)=1$ , then$c(G\bullet H)=1$ . If$c(G)=1$ ,$G$has more than one vertex, and$c(H)\geq 2$ , then$c(G\bullet H)=2$ . We also provide thecopnumberfor general lexicographic sums.  

【 授权许可】

Unknown