Let G = (V, E) be a graph. For any real valued function 1 : V --+ R and S ~ V, let 1 (S) = L:UES 1 ( u). The weight of 1 is defined as I(V). We will also denote I(N[v]) by I[v]' where v E V. A minus k-subdominating function (k8F) for G is defined in [1] as a function 1 : V --+ {-I, 0, I} such that I[v] 2:: 1 for at least k vertices of G. The minus k-subdomination number of a graph G, denoted by...

This article proposes a scenario-based algorithm for cluster formation and management in mobile ad hoc networks. Depending on the application a centralized or distributed algorithm based on (k, r) −Dominating Set is used for the selection of clusterheads and gateway nodes. Here k is the minimum number of clusterheads per node in the network and r is the maximum number of hops between the node a...

In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dominating set of G and the subgraph induced by S is connected. This is a basic connectivity problem that is known to be NP-complete, and it has been extensively studied using several algorithmic approaches. In this paper...

a {em roman dominating function} on a graph $g = (v ,e)$ is a function $f : vlongrightarrow {0, 1, 2}$ satisfying the condition that every vertex $v$ for which $f (v) = 0$ is adjacent to at least one vertex $u$ for which $f (u) = 2$. the {em weight} of a roman dominating function is the value $w(f)=sum_{vin v}f(v)$. the roman domination number of a graph $g$, denoted by $gamma_r(g)$, equals the...

An {em Italian dominating function} on a digraph $D$ with vertex set $V(D)$ is defined as a function$fcolon V(D)to {0, 1, 2}$ such that every vertex $vin V(D)$ with $f(v)=0$ has at least two in-neighborsassigned 1 under $f$ or one in-neighbor $w$ with $f(w)=2$. A set ${f_1,f_2,ldots,f_d}$ of distinctItalian dominating functions on $D$ with the property that $sum_{i=1}^d f_i(v)le 2$ for each $vi...

Let k ≥ 1 be an integer, and let G be a finite and simple graph with vertex set V (G). A signed total Italian k-dominating function (STIkDF) on a graph G is a functionf : V (G) → {−1, 1, 2} satisfying the conditions that $sum_{xin N(v)}f(x)ge k$ for each vertex v ∈ V (G), where N(v) is the neighborhood of $v$, and each vertex u with f(u)=-1 is adjacent to a vertex v with f(v)=2 or to two vertic...

Turnover is important for the maintenance and remodeling of the cytoskeleton during the processes of cell morphogenesis, mitosis and motility. Microtubule (MT) turnover is thought to occur by dynamic instability, growth and shortening at distal (plus) ends. Recent observation of MT release from the centrosome and depolymerization from proximal (minus) ends indicates the existence of a minus end...

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...