2012/04/20 by Lu, You, Xu, Jun-Ming
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1204.4514
Let p be a positive integer and G=(V,E) be a simple graph. A subset D⊆ V is a p-dominating set if each vertex not in D has at least p neighbors in D. The p-domination number \gp(G) is the minimum cardinality among all p-dominating sets of G. The p-bondage number bp(G) is the cardinality of a smallest set of edges whose removal from G results in a graph with a p-domination number greater than the p-domination number of G. In this note we determine the 2-domination number \g2 and 2-bondage number b2 for the grid graphs Gm,n=Pm× Pn for 2≤ m≤ 4.