A nonnegative signed dominating function (NNSDF) of a graph G is a function f from the vertex set V (G) to the set {−1, 1} such that ∑ u∈N [v] f(u) ≥ 0 for every vertex v ∈ V (G). The nonnegative signed domination number of G, denoted by γ s (G), is the minimum weight of a nonnegative signed dominating function on G. In this paper, we establish some sharp lower bounds on the nonnegative signed ...

We present a simple heuristic for finding a small connected dominating set of cubic graphs. The average-case performance of this heuristic, which is a randomised greedy algorithm, is analysed on random n-vertex cubic graphs using differential equations. In this way, we prove that the expected size of the connected dominating set returned by the algorithm is asymptotically almost surely less tha...

We consider the problem of finding a spanning tree that maximizes the number of leaves (MaxLeaf). We provide a 3/2-approximation algorithm for this problem when restricted to cubic graphs, improving on the previous 5/3-approximation for this class. To obtain this approximation we define a graph parameter x(G), and construct a tree with at least (n−x(G)+4)/3 leaves, and prove that no tree with m...

We give efficient deterministic distributed algorithms which given a graph G from a proper minor-closed family C find an approximation of a minimum dominating set in G and a minimum connected dominating set in G. The algorithms are deterministic and run in a polylogarithmic number of rounds. The approximation accomplished differs from an optimal by a multiplicative factor of (1 + o(1)).

In this paper, we study the Dominating Set problem in random graphs. In a random graph, each pair of vertices are joined by an edge with a probability of p, where p is a positive constant less than 1. We show that, given a random graph in n vertices, a minimum dominating set in the graph can be computed in expected 2 2 2 n) time. For the parameterized dominating set problem, we show that it can...

In this paper, we consider the dominance properties of the set of the pignistic k-additive belief functions. Then, given k, we conjecture the shape of the polytope of all the k-additive belief functions dominating a given belief function, starting from an analogy with the case of dominating probability measures. Under such conjecture, we compute the analytical form of the barycenter of the poly...

In this paper, we consider r-dominating cliques in homogeneously orderable graphs (a common generalization of dually chordal and distance-hereditary graphs) and their relation to strict r-packing sets. We prove that a homogeneously orderable graph G possesses an r-dominating clique if and only if for any pair of vertices x , y of G d (x , y ) ° r ( x ) / r ( y ) / 1 holds where r : V r N is a g...

AIMS The aim is to compare the coronary risk chart published by the European Task Force for Prevention of Coronary Heart Disease and produced using a Framingham risk function, with a risk function derived from an Italian population study. METHODS AND RESULTS Coronary risk function in this study was the result of longitudinal experience in an Italian middle-aged population of 1656 male subject...

Let D be a finite and simple digraph with the vertex set V (D), and let f : V (D) → {−1, 1} be a two-valued function. If∑ x∈N[v] f(x) ≥ 1 for each v ∈ V (D), where N[v] consists of v and all vertices of D from which arcs go into v, then f is a signed dominating function on D. The sum f(V (D)) is called the weight w(f) of f . The minimum of weights w(f), taken over all signed dominating function...