A complex unit gain graph ( T -gain graph) Φ = G , φ ) is a where the function assigns number to each orientation of an edge and its inverse assigned opposite orientation. balanced if product gains oriented cycle (if any) 1. We propose two notions distance matrices D < max min Φ, for any ordering ‘<’ vertex set. characterize graphs which are independent ordering. show holds standard vertices on...

We present a polynomial-time approximation scheme (PTAS) for the minimum dominating set problem in unit disk graphs. In contrast to previously known approximation schemes for the minimum dominating set problem on unit disk graphs, our approach does not assume a geometric representation of the vertices (specifying the positions of the disks in the plane) to be given as part of the input. The alg...

Broadcasting is the information dissemination process in a communication network. A subset of processors V, c Vcalled originators knows an unique message which has to be transferred by calls between adjacent processors. Each call requires one time unit and each processor can participate in at most one call per time unit. The problem is to find a schedule such that the time needed to inform all ...

In this paper we study a problem occuring in the context of geometric routing algorithms for mobile ad-hoc networks: Finding unit disk graph coordinates given a graph G = (V, E). Based on a proof that recognition of unit disk graphs is an NP-hard problem, we show that the problem of finding unit disk graph coordinates given a graph G = (V, E) is NPhard. Subsequently, we show that the proof does...