﻿ Lower bounds on the signed (total) \$k\$-domination number

# Lower bounds on the signed (total) \$k\$-domination number

##### چکیده

Let \$G\$ be a graph with vertex set \$V(G)\$. For any integer \$kge 1\$, a signed (total) \$k\$-dominating functionis a function \$f: V(G) rightarrow { -1, 1}\$ satisfying \$sum_{xin N[v]}f(x)ge k\$ (\$sum_{xin N(v)}f(x)ge k\$)for every \$vin V(G)\$, where \$N(v)\$ is the neighborhood of \$v\$ and \$N[v]=N(v)cup{v}\$. The minimum of the values\$sum_{vin V(G)}f(v)\$, taken over all signed (total) \$k\$-dominating functions \$f\$, is called the signed (total)\$k\$-domination number. The clique number of a graph \$G\$ is the maximum cardinality of a complete subgraph of \$G\$.In this note we present some new sharp lower bounds on the signed (total) \$k\$-domination numberdepending on the clique number of the graph. Our results improve some known bounds.

برای دانلود باید عضویت طلایی داشته باشید

برای دسترسی به متن کامل این مقاله و 10 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

## New bounds on the signed total domination number of graphs

In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turán [8], we present a sharp lower bound on Kr+1-free graphs for r ≥ 2. Applying the concept of total limited packing we bound the signed total domination number of G with δ(G) ≥ 3 from above by n−2b 2ρo(G)+δ−3...

متن کامل

## On the Signed (Total) \$k\$-Domination Number of a Graph

Let k be a positive integer and G = (V,E) be a graph of minimum degree at least k − 1. A function f : V → {−1, 1} is called a signed k-dominating function of G if ∑ u∈NG[v] f(u) ≥ k for all v ∈ V . The signed k-domination number of G is the minimum value of ∑ v∈V f(v) taken over all signed k-dominating functions of G. The signed total k-dominating function and signed total k-domination number o...

متن کامل

## Signed total Italian k-domination in graphs

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...

متن کامل

## Upper Bounds on the Total Domination Number

A total dominating set of a graph G with no isolated vertex is a set S of vertices of G such that every vertex is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set in G. In this paper, we present several upper bounds on the total domination number in terms of the minimum degree, diameter, girth and order.

متن کامل

## Signed total Roman k-domination in directed graphs

Let \$D\$ be a finite and simple digraph with vertex set \$V(D)\$‎.‎A signed total Roman \$k\$-dominating function (STR\$k\$DF) on‎‎\$D\$ is a function \$f:V(D)rightarrow{-1‎, ‎1‎, ‎2}\$ satisfying the conditions‎‎that (i) \$sum_{xin N^{-}(v)}f(x)ge k\$ for each‎‎\$vin V(D)\$‎, ‎where \$N^{-}(v)\$ consists of all vertices of \$D\$ from‎‎which arcs go into \$v\$‎, ‎and (ii) every vertex \$u\$ for which‎‎\$f(u)=-1\$ has a...

متن کامل

## Bounds on the Inverse Signed Total Domination Numbers in Graphs

Abstract. Let G = (V,E) be a simple graph. A function f : V → {−1, 1} is called an inverse signed total dominating function if the sum of its function values over any open neighborhood is at most zero. The inverse signed total domination number of G, denoted by γ0 st(G), equals to the maximum weight of an inverse signed total dominating function of G. In this paper, we establish upper bounds on...

متن کامل

ذخیره در منابع من

ذخیره شده در منابع من

با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی راحت تر خواهید کرد

دانلود متن کامل

برای دسترسی به متن کامل این مقاله و 10 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره 3  شماره 2

صفحات  173- 178

تاریخ انتشار 2018-12-01

{@ msg @}

با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.

کلمات کلیدی

میزبانی شده توسط پلتفرم ابری doprax.com