Trees with equal 2-domination and 2-independence numbers | Zendy

Mustapha Chellali | Zendy; Nacéra Meddah | Zendy

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Trees with equal 2-domination and 2-independence numbers

Author(s) -

Mustapha Chellali,

Nacéra Meddah

Publication year - 2012

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.1603

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

Let G = (V,E) be a graph. A subset S of V is a 2-dominating set if every vertex of V S is dominated at least 2 times, and S is a 2-independent set of G if every vertex of S has at most one neighbor in S. The minimum cardinality of a 2-dominating set a of G is the 2-domination number 2(G) and the maximum cardinality of a 2-independent set of G is the 2-independence number 2(G). Fink and Jacobson proved that 2(G) 2(G) for every graph G. In this paper we provide a constructive characterization of trees with equal 2-domination and 2-independence numbers.

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