We study network coding for multi-hop wireless networks. We focus the case of broadcasting, where one source transmits information to all the nodes in the network. Our goal is energy-efficient broadcasting, in other words, to minimize the number of transmissions for broadcasting to the entire network. To achieve this goal, we propose a family of methods that combine the use of network coding an...

Communication protocols for mobile ad hoc networks (MANETs) follow either an Optimum Routing Approach (ORA) or the Least Overhead Routing Approach (LORA): With ORA, protocols tend to determine and use the optimal communication structure at every time instant; whereas with LORA, a protocol tends to use a chosen communication structure as long as it exists. In this paper, we study the impact of t...

For a graph G=(V,E) with V=V(G) and E=E(G), perfect double Italian dominating function is f:V→{0,1,2,3} having the property that 3≤∑u∈NG[v]f(u)≤4, for every vertex v∈G f(v)∈{0,1}. The weight of f sum f(V)=∑v∈V(G)f(v) minimum on G domination number γdIp(G) G. We initiate study functions. check γdIp some standard graphs evaluate γdI such graphs. functions versus Roman are perused. NP-completeness...

A function f : V (G) → {−1, 0, 1} is a minus dominating function if for every vertex v ∈ V (G), ∑ u∈N [v] f(u) ≥ 1. A minus dominating function f of G is called a global minus dominating function if f is also a minus dominating function of the complement G of G. The global minus domination number γ− g (G) of G is defined as γ − g (G) = min{ ∑ v∈V (G) f(v) | f is a global minus dominating functi...

A double Roman dominating function on a graph G=(V,E) is f:V?{0,1,2,3} with the properties that if f(u)=0, then vertex u adjacent to at least one assigned 3 or two vertices 2, and f(u)=1, 2 3. The weight of f equals w(f)=?v?Vf(v). domination number ?dR(G) G minimum G. said be ?dR(G)=3?(G), where ?(G) We obtain sharp lower bound generalized Petersen graphs P(3k,k), we construct solutions providi...

‎for any integer $kge 1$‎, ‎a minus $k$-dominating function is a‎ ‎function $f‎ : ‎v (g)rightarrow {-1,0‎, ‎1}$ satisfying $sum_{win‎‎n[v]} f(w)ge k$ for every $vin v(g)$‎, ‎where $n(v) ={u in‎‎v(g)mid uvin e(g)}$ and $n[v] =n(v)cup {v}$‎. ‎the minimum of‎‎the values of $sum_{vin v(g)}f(v)$‎, ‎taken over all minus‎‎$k$-dominating functions $f$‎, ‎is called the minus $k$-domination‎‎number and i...

This paper addresses the problem of scatternet formation and maintenance for multi-hop Bluetooth based personal area and ad hoc networks with minimal communication overhead. Each node is assumed to know its position and position of all its neighbours. The proposed formation algorithms have three phases. In the first phase the unit graph is constructed (each node establishes connection with all ...

One of the important issues in wireless networks is the Routing problem that is effective on system performance, in this article the attempt is made to propose a routing algorithm using the bee colony in order to reduce energy consumption in wireless relay networks. In EBCD algorithm, through combined of energy, distance and traffic parameters a routing algorithm for wireless networks is presen...


 Let G be a connected graph. A set S of vertices in is 2-resolving hop dominating if and for every vertex x ∈ V (G)\S there exists y such that dG(x, y) = 2. The minimum cardinality called the domination number denoted by γ2Rh(G). This study aims to combine concept with sets graphs. main results generated this include characterization join, corona lexicographic product two graphs, as well ...