Let G be a graph with vertex set V (G) and edge set E(G). A defensive alliance in G is a subset S of V (G) such that for every vertex v ∈ S, |N [v] ∩ S| ≥ |(V (G)−N [v]) ∩ S|. A global defensive alliance is an alliance that is also a dominating set. We define the alliance partition number, ψa(G) (global alliance partition number, ψg(G)), to be the maximum number of sets in a partition of V (G) ...

This study aims to explore Turkish citizen-consumers' understanding of and reactions to censorship of websites in Turkey by using in-depth interviews and online ethnography. In an environment where sites such as YouTube and others are increasingly being banned, the citizen-consumers' macro-level understanding is that such censorship is part of a wider ideological plan and their micro-level unde...

A Roman dominating function on a graph G = (V, E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V ) = ∑ u∈V f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. In this pape...

A global offensive alliance in a graph G is a set S of vertices with the property that every vertex not belonging to S has at least one more neighbor in S than it has outside of S. The global offensive alliance number of G, γo(G), is the minimum cardinality of a global offensive alliance in G. A set S of vertices of a graph G is a dominating set for G if every vertex not belonging to S has at l...

A Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V (G)) = ∑ u∈V (G) f(u). The Roman domination number of G, γR(G), is the minimum weight of a Roman dominating function on G. In this paper, we...

A Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V (G)) = ∑ u∈V (G) f(u). The Roman domination number γR(G) of G is the minimum weight of a Roman dominating function on G. In this paper, we s...

We investigate the relationship between global offensive k-alliances and some characteristic sets of a graph including r-dependent sets, τ dominating sets and standard dominating sets. In addition, we discuss the close relationship that exist among the (global) offensive ki-alliance number of Γi, i ∈ {1, 2} and the (global) offensive k-alliance number of Γ1×Γ2, for some specific values of k. As...

Given an undirected graph G = (V,E) and a weight function w : E → R, the Minimum Dominating Tree problem asks to find a minimum weight sub-tree of G, T = (U,F ), such that every v ∈ V \U is adjacent to at least one vertex in U . The special case when the weight function is uniform is known as the Minimum Connected Dominating Set problem. Given an undirected graph G = (V,E) with some subsets of ...