We study the problem of predicting the state of a vertex in automata networks, where the
state at each site is given by the majority function over its neighborhood. We show that for …

In this paper, we obtain several tight bounds of the defensive k-alliance number in the
complement graph from other parameters of the graph. In particular, we investigate the …

Alliances are used to denote agreements between members of a group with similar
interests. Alliances can occur between nations, biological sequences, business cartels, and …

A set $ S $ of vertices of a graph $ G $ is a defensive $ k $-alliance in $ G $ if every vertex of
$ S $ has at least $ k $ more neighbors inside of $ S $ than outside. This is primarily an …

A defensive alliance in a graph G=(V, E) is a set of vertices S satisfying the condition that
every vertex v∈ S has at least as many neighbors (including itself) in S than it has in V∖ S …

A defensive alliance in a graph G=(V, E) G=(V, E) is a set of vertices S satisfying the
condition that every vertex v ∈ S v∈ S has at least as many neighbours (including itself) in …

A defensive alliance in an undirected graph G=(V, E) is a nonempty set of vertices S
satisfying the condition that every vertex v∈ S has at least as many neighbours (including …

The information diffusion has been modeled as the spread of an information within a group
through a process of social influence, where the diffusion is driven by the so called …

We investigate the natural situation of the dissemination of information on various graph
classes starting with a random set of informed vertices called active. Initially active vertices …

In this paper we study defensive alliances in some regular graphs. We determine which
subgraphs could a critical defensive alliance of a graph $ G $ induce, if $ G $ is $6 $-regular …