A characterization of trees with equal independent domination and secure domination numbers

Let i(G) and γs(G) be the independent domination number and secure domination number of a graph G, respectively. Merouane and Chellali (2015) [12] proved that i(T)≤γs(T) for any tree T and asked to characterize the trees T with i(T)=γs(T). In this paper, we answer the question. We introduce three operations on trees and prove that any tree T with i(T)=γs(T) can be obtained by these operations.