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)).

OBJECTIVE Our purpose was to describe the surgical procedure, its results, and its complications and to determine whether patients are satisfied with surgical reduction of labia minora in cases of hypertrophy. STUDY DESIGN The records of 163 patients who underwent reduction of the labia minora during a 9-year period were reviewed. The ages of the patients ranged from 12 to 67 years (median, 2...

INTRODUCTION Limited information is available regarding patients' indication for seeking labiaplasty of the labia minora. AIM The aim of this article is to investigate a patient's indications for seeking labiaplasty of the labia minora. METHODS This is a retrospective review of the medical records of all patients undergoing labiaplasty at our clinic over a 27-month period. MAIN OUTCOME ME...

In this paper we consider a kind of higher-order evolution equation as^{kt^{k} + ^{k&minus1}u/t^{k&minus1} +• • •+ut &minus{delta}u= f (u, {delta}u,x). For this equation, we investigate nonglobal solution, blow-up in finite time and instantaneous blow-up under some assumption on k, f and initial data. In this paper we employ the Test function method, the eneralized convexity method an...

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...