A Connected Dominating Set (CDS) of the graph representing a Wireless Sensor Network can be used as a virtual backbone for routing in the network. Since sensor nodes are constrained by limited on-board batteries, it is desirable to have a small CDS for the network. However, constructing a minimum size CDS has been shown to be a NP-hard problem. In this paper we present a distributed greedy algo...

For any integer  ‎, ‎a minus  k-dominating function is a‎function  f‎ : ‎V (G)  {-1,0‎, ‎1} satisfying w) for every  vertex v, ‎where N(v) ={u V(G) | uv  E(G)}  and N[v] =N(v)cup {v}. ‎The minimum of ‎the values of  v)‎, ‎taken over all minus‎k-dominating functions f,‎ is called the minus k-domination‎number and is denoted by $gamma_k^-(G)$ ‎. ‎In this paper‎, ‎we ‎introduce the study of minu...

plants in ancient fictional texts describe the  relation between low world and super worlds and appear in forms including ritual resurrection, human reincarnation in plant and vice versa, identification of human and plant , and etc which  relate human's spirit to supernatural. contemporary persian poets are taking advantage of a new language that is full of mythical concepts for expression...


 Let G be a connected graph. A set S ⊆ V (G) is restrained 2-resolving hop dominating of if and = or ⟨V (G)\S⟩ has no isolated vertex. The domination number G, denoted by γr2Rh(G) the smallest cardinality G. This study aims to combine concept with sets graphs. main results generated in this include characterization join, corona, edge corona lexicographic product graphs, as well their corr...

Let G be an undirected graph with vertex and edge sets V (G) E(G), respectively. A set S ⊆ is called a hop independent dominating of if both G. The minimum cardinality G, denoted by γhih(G), the domination number In this paper, we show that lies between independence We characterize these types in shadow graph, join, corona, lexicographic product two graphs. Moreover, either exact values or boun...

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...

Wireless ad hoc networks are advancing rapidly, both in research and more and more into our everyday lives. Wireless sensor networks are a prime example of a new technology that has gained a lot of attention in the literature, and that is going to enhance the way we view and interact with the environment. These ad hoc and sensor networks are modeled by communication graphs which give the commun...

In mobile ad hoc networks (MANETs), networks can be partitioned into clusters. Clustering algorithms are localized algorithms that have the property of creating an upper bounded clusterheads in any networks even in the worst case. Generally, clusterheads and selected gateways form a connected dominating set (CDS) of the network. This CDS forms the backbone of the network and can be used for rou...

A set S ⊆ V (G) is a restrained strong resolving hop dominating in G if for every v ∈ (G)\S, there exists w such that dG(v, w) = 2 and or (G)\S has no isolated vertex. The smallest cardinality of set, denoted by γrsRh(G), called the domination number G. In this paper, we obtained corresponding parameter graphs resulting from join, corona lexicographic product two graphs. Specifically, character...