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- Title
A new upper bound on the independent 2-rainbow domination number in trees.
- Authors
Gholami, Elham; Rad, Nader Jafari; Tehranian, Abolfazl; Rasouli, Hamid
- Abstract
A 2-rainbow dominating function on a graph G is a function g that assigns to each vertex a set of colors chosen from the subsets of f1; 2g so that for each vertex with g(v) =; we have S u2N(v) g(u) = f1; 2g. The weight of a 2-rainbow dominating function g is the value w(g) = P v2V (G) jf(v)j. A 2-rainbow dominating function g is an independent 2-rainbow dominating function if no pair of vertices assigned nonempty sets are adjacent. The 2-rainbow domination number r2(G) (respectively, the inde-pendent 2-rainbow domination number ir2(G)) is the minimum weight of a 2-rainbow dominating function (respectively, independent 2-rainbow dominating function) on G. We prove that for any tree T of order ≥ 3, with l leaves and s support vertices, ir2(T) ≤ (14n + ' + s)=20, thus improving the bound given in [Independent 2-rainbow domination in trees, Asian-Eur. J. Math. 8 (2015) 1550035] under certain conditions.
- Subjects
GRAPHIC methods; CHARTS, diagrams, etc.; MATHEMATICS; GEOMETRIC vertices; APPLIED mathematics
- Publication
Communications in Combinatorics & Optimization, 2023, Vol 8, Issue 1, p261
- ISSN
2538-2128
- Publication type
Article
- DOI
10.22049/CCO.2022.27641.1305