Bounds on the disjunctive domination number of a tree

School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, P.R. China

^* Corresponding author: zhuangweixmu@163.com

Received: 3 February 2020
Accepted: 15 June 2022

Abstract

A set D of vertices in a graph G is a disjunctive dominating set in G if every vertex not in D is adjacent to a vertex of D or has at least two vertices in D at distance 2 from it in G. The disjunctive domination number, γ^d₂(G), of G is the minimum cardinality of a disjunctive dominating set in G. We show that if T is a tree of order n with l leaves and s support vertices, then n-l+3/4≤γ^d₂(T)≤n+l+s/4. Moreover, we characterize the families of trees which attain these bounds.