Given a set P of n points in the plane, we solve the problems of constructing a geometric planar graph spanning P 1) of minimum degree 2, and 2) which is 2-edge connected, respectively, and has max edge length bounded by a factor of 2 times the optimal; we also show that the factor 2 is best possible given appropriate connectivity conditions on the set P, respectively. First, we construct in O(...

Many prominent applications in wireless sensor networks require collected information has to be routed to end nodes in an efficient manner. In general, Connected Dominating Set (CDS) based routing is a promising approach for enhancing the routing efficiency in sensor networks. Our idea is to generate a quality based CDS algorithm, which can resolve the standing issues like cardinality, risk fac...

Connected Dominating Set (CDS) has been a well known approach for constructing a virtual backbone to alleviate the broadcasting storm in wireless networks. Previous literature modeled the wireless network in a 2-dimensional plane and looked for the approximated Minimum CDS (MCDS) distributed or centralized to construct the virtual backbone of the wireless network. However, in some real situatio...

3 Energy efficient broadcasting without range adjustment 10 3.1 Clustering based broadcasting protocols . . . . . . . . . . . . . . . . 11 3.2 Neighbor elimination based broadcasting protocols . . . . . . . . . . 11 3.3 Distance-based and probabilistic protocols . . . . . . . . . . . . . . . 11 3.4 Coverage and connected dominating set based broadcasting . . . . . 12 3.5 Forwarding neighbors ba...

the concept of the bipartite divisor graph for integer subsets has been considered in [‎graph combinator., ‎ 26 (2010) 95--105‎.]. ‎in this paper‎, ‎we will consider this graph for the set of character degrees of a finite group $g$ and obtain some properties of this graph‎. ‎we show that if $g$ is a solvable group‎, ‎then the number of connected components of this graph is at most $2$ and if $g...

Let $G$ be a finite group and $cd^*(G)$ be the set of nonlinear irreducible character degrees of  $G$. Suppose that $rho(G)$ denotes the set of primes dividing some element of $cd^*(G)$. The bipartite divisor graph for the set of character degrees which is denoted by $B(G)$, is a bipartite graph whose vertices are the disjoint union of $rho(G)$ and $cd^*(G)$, and a vertex $p in rho(G)$ is conne...