Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Opuscula Mathematica

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: global offensive k-alliance number

Sortuj według:

Ogranicz wyniki do:

Global offensive k-alliance in bipartite graphs

Chellali M., Volkmann L.

Opuscula Mathematica

2012

Vol. 32, no. 1

83-89

Let k ≥ 0 be an integer. A set S of vertices of a graph G = (V (G), E(G)) is called a global offensive k-alliance if /N(v) ∩ S/ ≥ /N(v) - S/ + k for every v ∈ V (G) - S, where 0 ≤ k Δ and Δ is the maximum degree of G. The global offensive k-alliance number [formula] is the minimum cardinality of a global offensive k-alliance in G. We show that for every bipartite graph G and every integer k ≥ 2, [formula], where Lk(G) is the set of vertices of degree at most k - 1. Moreover, extremal trees attaining this upper bound are characterized.

Trees with equal global offensive k-alliance and k-domination numbers

Chellali M.

Opuscula Mathematica

2010

Vol. 30, no. 3

249-254

Let k ≥ 1 be an integer. A set S of vertices of a graph G = (V (G), E(G)) is called a global offensive k-alliance if |N(v) ∩ S| ≥ |N(v) - S| + k for every v ∈ V (G) - S, where N(v) is the neighborhood of v. The subset S is a k-dominating set of G if every vertex in V (G) - S has at least k neighbors in S. The global offensive k-alliance number [formula] is the minimum cardinality of a global offensive k-alliance in G and the k-domination number ϒ k(G) is the minimum cardinality of a k-dominating set of G. For every integer k ≥ 1 every graph G satisfies [formula]. In this paper we provide for k ≥ 2 a characterization of trees T with equal [formula] and ϒ k(T).