Let G be a connected graph. A set W ⊆ V (G) is resolving hop dominating of if in and for every vertex v ∈ \ there exists u such that dG(u, v) = 2. S 1-movable S, either {v} or ((V S) ∩ NG(v)) (S {v}) ∪ {u} G. The domination number G, denoted by γ 1 mRh(G) the smallest cardinality This paper presents characterization sets join, corona lexicographic product graphs. Furthermore, this determines ex...

To increase the positioning accuracy of Distance Vector-Hop (DV-Hop) algorithm in non-uniform networks, an improved DV-Hop based on RSSI correction is proposed. The new first quantizes hops between two nodes by ratio value and benchmark value, divides continuously, calculates average hop distance according to Minimum Mean Square Error (MMSE) criterion best index quantized hops, then adds matchi...

A set S is a 1-movable strong resolving hop dominating of G if for every v ∈ S, either S\{v} or there exists vertex u (V (G)\S)∩NG(v) such that (S \ {v}) ∩ {u} G. The minimum cardinality denoted by γ 1 msRh(G). In this paper, we obtained the corresponding parameter in graphs resulting from join, corona and lexicographic product two graphs. Specifically, characterize sets these types determine b...

Let $kgeq 1$ be an integer, and let $G$ be a graph. A {it$k$-rainbow dominating function} (or a {it $k$-RDF}) of $G$ is afunction $f$ from the vertex set $V(G)$ to the family of all subsetsof ${1,2,ldots ,k}$ such that for every $vin V(G)$ with$f(v)=emptyset $, the condition $bigcup_{uinN_{G}(v)}f(u)={1,2,ldots,k}$ is fulfilled, where $N_{G}(v)$ isthe open neighborhood of $v$. The {it weight} o...

Abstract Background: Despite the importance of functional-performance deficits in athletes with history of ankle sprain few, studies have been carried out in this area. The aim of this research was to study relationship between previous ankle sprains and functional-performance deficits in athletes. Materials and methods: The subjects were 40 professional athletes selected through random sampl...

A vertex w in a connected graph G strongly resolves two distinct vertices u and v V (G) if is any shortest u-w path or v-w path. set W of strong resolving every are resolved by some W. S subset hop dominating for ∈ \ there exists such that dG(u, v) = 2. The smallest cardinality called the domination number G. This paper presents characterization sets join, corona lexicographic product graphs. F...

In this paper, we define a new domination-like invariant of graphs. Let $${\mathbb {R}}^{+}$$ be the set non-negative numbers. $$c\in {\mathbb {R}}^{+}-\{0\}$$ number, and let G graph. A function $$f:V(G)\rightarrow is c-self-dominating if for every $$u\in V(G)$$ , $$f(u)\ge c$$ or $$\max \{f(v):v\in N_{G}(u)\}\ge 1$$ . The c-self-domination number $$\gamma ^{c}(G)$$ defined as ^{c}(G):=\min \{...

This paper presents a new power conservation scheme for multi-hop ad hoc networks. A virtual backbone consisting of special nodes (coordinators) is used for the power saving algorithm and routing. We present a novel algorithm for constructing a connected dominating set (CDS) that is used to construct and maintain the virtual backbone of the network. Our scheme includes a message history based v...