Domination, independent domination number and 2-independence number in trees | Zendy

H. Aram | Zendy; Nasrin Dehgardi | Zendy; Seyed Mahmoud Sheikholeslami | Zendy; Mina Valinavaz | Zendy; Lutz Volkmann | Zendy

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Domination, independent domination number and 2-independence number in trees

Author(s) -

H. Aram,

Nasrin Dehgardi,

Seyed Mahmoud Sheikholeslami,

Mina Valinavaz,

Lutz Volkmann

Publication year - 2018

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.2165

Subject(s) - mathematics , domination analysis , independence number , independence (probability theory) , combinatorics , statistics , graph , vertex (graph theory)

For a graph G, let γ(G) be the domination number, i(G) be the independent domination number and β2(G) be the 2-independence number. In this paper, we prove that for any tree T of order n ≥ 2, 4β2(T) − 3γ(T) ≥ 3i(T), and we characterize all trees attaining equality. Also we prove that for every tree T of order n ≥ 2, i(T)≤3β2(T)4 i(T) \le {{3{\beta _2}(T)} \over 4} , and we characterize all extreme trees.

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