Volume 57, Number 4, July-August 2023
|Page(s)||1951 - 1956|
|Published online||24 July 2023|
A new lower bound for the independent domination number of a tree
Universidad de Córdoba, Departamento de Matemáticas, Campus de Rabanales, 14071 Córdoba, Spain
* Corresponding author: email@example.com
Accepted: 11 July 2023
A set D of vertices in a graph G is an independent dominating set of G if D is an independent set and every vertex not in D is adjacent to a vertex in D. The independent domination number of G, denoted by i(G), is the minimum cardinality among all independent dominating sets of G. In this paper we show that if T is a nontrivial tree, then i(T) ≥ n(T)+γ(T)−l(T)+2/4, where n(T), γ(T) and l(T) represent the order, the domination number and the number of leaves of T, respectively. In addition, we characterize the trees achieving this new lower bound.
Mathematics Subject Classification: 05C69 / 05C05
Key words: Independent domination number / Domination number / Trees
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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