the minus k-domination numbers in graphs
نویسندگان
چکیده
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 is denoted by $gamma^-_{k}(g)$. in this paper, weintroduce the study of minus $k$-domination in graphs and we presentseveral sharp lower bounds on the minus $k$-domination number for general graphs.
منابع مشابه
The minus k-domination numbers in graphs
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...
متن کاملTotal $k$-Rainbow domination numbers in graphs
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...
متن کاملMinus domination number in k-partite graphs
A function f de1ned on the vertices of a graph G = (V; E); f :V → {−1; 0; 1} is a minus dominating function if the sum of its values over any closed neighborhood is at least one. The weight of a minus dominating function is f(V ) = ∑ v∈V f(v). The minus domination number of a graph G, denoted by −(G), equals the minimum weight of a minus dominating function of G. In this paper, a sharp lower bo...
متن کاملTotal minus domination in k-partite graphs
A function f defined on the vertices of a graph G = (V ,E), f : V → {−1, 0, 1} is a total minus dominating function (TMDF) if the sum of its values over any open neighborhood is at least one. The weight of a TMDF is the sum of its function values over all vertices. The total minus domination number, denoted by −t (G), of G is the minimum weight of a TMDF on G. In this paper, a sharp lower bound...
متن کاملTwin minus domination in directed graphs
Let $D=(V,A)$ be a finite simple directed graph. A function$f:Vlongrightarrow {-1,0,1}$ is called a twin minus dominatingfunction (TMDF) if $f(N^-[v])ge 1$ and $f(N^+[v])ge 1$ for eachvertex $vin V$. The twin minus domination number of $D$ is$gamma_{-}^*(D)=min{w(f)mid f mbox{ is a TMDF of } D}$. Inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lo...
متن کاملMinus edge k-subdomination numbers in graphs
The closed neighborhood NG[e] of an edge e in a graph G is the set consisting of e and of all edges having a common end-vertex with e. Let f be a function on E(G), the edge set of G, into the set {−1, 0, 1}. If ∑ x∈N [e] f(x) ≥ 1 for at least k edges e of G, then f is called a minus edge k-subdominating function of G. The minimum of the values ∑ e∈E(G) f(e), taken over all minus edge k-subdomin...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
communication in combinatorics and optimizationجلد ۱، شماره ۱، صفحات ۱۵-۲۸
کلمات کلیدی
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023