This paper addresses the scatternet formation for large scale multi-hop Bluetooth networks. We first describe an efficient method to build a Connected Dominating Set (CDS) as the backbone of multi-hop Bluetooth network, then propose new algorithms to form the dBBlue scatternets (Song et al., 2005) in each cluster. The final scatternet, M-dBBlue, guarantees the connectivity. Our experiment shows...

In this paper, we introduce and do an initial investigation of a variant Grundy hop domination in graph called the connected domination. We show that number lies between graph. particular, give realization results involving domination, numbers. Moreover, determine numbers some graphs.

Let G be an undirected graph with vertex and edge sets V (G) E(G), respectively. A subset S of vertices is a geodetic hop dominating set if it both set. The domination number G, γhg(G), the minimum cardinality among all in G. Geodetic resulting from some binary operations have been characterized. These characterizations used to determine tight bounds for each graphs considered.

Let G be an undirected connected graph with vertex and edge sets V (G) E(G), respectively. A set C ⊆ is called weakly convex hop dominating if for every two vertices x, y ∈ C, there exists x-y geodesic P(x, y) such that (P(x, y)) v (G)\C, w dG(v, w) = 2. The minimum cardinality of a G, denoted by γwconh(G), the domination number G. In this paper, we introduce initially investigate concept domin...

In large wireless multi-hop networks, routing is a main issue as they include many nodes that span over relatively a large area. In such a scenario, finding smallest set of dominant nodes for forwarding packets would be a good approach for better communication. Connected dominating set (CDS) computation is one of the method to find important nodes in the network. As CDS computation is an NP pro...

A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...

An ad hoc network may be logically represented as a set of clusters. The clusterheads form a d-hop dominating set. Each node is at most d hops from a clusterhead. Clusterheads form a virtual backbone and may be used to route packets for nodes in their cluster. Previous heuristics restricted themselves to 1-hop clusters. We show that the minimum d-hop dominating set problem is NP-complete. Then ...

a set $s$ of vertices in a graph $g$ is a dominating set if every vertex of $v-s$ is adjacent to some vertex in $s$. the domination number $gamma(g)$ is the minimum cardinality of a dominating set in $g$. the annihilation number $a(g)$ is the largest integer $k$ such that the sum of the first $k$ terms of the non-decreasing degree sequence of $g$ is at most the number of edges in $g$. in this p...