2013/09/05 by Lemańska, M., Swaminathan, V., Venkatakrishnan, Y. B. +1 · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1309.1315
Let G=(V,E) be a graph. A subset D of V(G) is called a super dominating set if for every v ∈ V(G)-D there exists an external private neighbour of v with respect to V(G)-D. The minimum cardinality of a super dominating set is called the super domination number of G and is denoted by γsp(G). In this paper some results on the super domination number are obtained. We prove that if T is a tree with at least three vertices, then (n)/(2)≤γsp(T)≤ n-s, where s is the number of support vertices in T and we characterize the extremal trees.