A 2-rainbow dominating function ( ) of a graph  is a function  from the vertex set  to the set of all subsets of the set  such that for any vertex  with  the condition  is fulfilled, where  is the open neighborhood of . A maximal 2-rainbow dominating function on a graph  is a 2-rainbow dominating function  such that the set is not a dominating set of . The weight of a maximal    is the value . ...

We propose a novel randomized algorithm for computing a dominating set based clustering in wireless ad-hoc and sensor networks. The algorithm works under a model which captures the characteristics of the set-up phase of such multi-hop radio networks: asynchronous wake-up, the hidden terminal problem, and scarce knowledge about the topology of the network graph. When modelling the network as a u...

The efficiency of a communication network depends not only on its control protocols, but also on the underlying network topology. We propose a distributed topology management algorithm that constructs and maintains a backbone topology based on a minimal dominating set (MDS) of the network. According to this algorithm, each node determines the membership in the MDS for itself and its one-hop nei...

Wireless sensor networks (WSNs) consist of battery-constrained sensors often deployed in harsh environments with little to no human control, thereby necessitating scalable and energy-efficient techniques. For this reason, self-organizing and maintenance mechanisms are very appealing to the design of WSNs. In this paper, we propose a routing scheme, called WCDSDCR, that meets these design requir...

This paper is devoted to the study of quadruple Roman domination in trees, and it a contribution Special Issue “Theoretical computer science discrete mathematics” Symmetry. For any positive integer k, [k]-Roman dominating function ([k]-RDF) simple graph G from vertex set V {0,1,2,…,k+1} if for u?V with f(u)<k, ?x?N(u)?{u}f(x)?|{x?N(u):f(x)?1}|+k, where N(u) open neighborhood u. The weight [k...

Let G = (V,E) be a graph and let f be a function f : E → {0, 1, 2}. An edge x with f(x) = 0 is said to be undefended with respect to f if it is not incident to an edge with positive weight. The function f is a weak edge Roman dominating function (WERDF) if each edge x with f(x) = 0 is incident to an edge y with f(y) > 0 such that the function f ′ : E → {0, 1, 2}, defined by f ′(x) = 1, f ′(y) =...

Let G be a graph with no isolated vertex and f : V ( ) → {0, 1, 2} function. i = { x ∈ } for every . We say that is total Roman dominating function on if in 0 adjacent to at least one 2 the subgraph induced by 1 ∪ has vertex. The weight of ω ∑ v minimum among all functions domination number , denoted γ t R It known general problem computing NP-hard. In this paper, we show H nontrivial graph, th...