﻿ Outer independent Roman domination number of trees

# Outer independent Roman domination number of trees

##### نویسندگان
• M Chellali LAMDA-RO Laboratory, Department of Mathematics University of Blida B.P. 270, Blida, Algeria
##### چکیده

‎A Roman dominating function (RDF) on a graph G=(V,E) is a function  f : V → {0, 1, 2}  such that every vertex u for which f(u)=0 is‎ ‎adjacent to at least one vertex v for which f(v)=2‎. ‎An RDF f is called‎‎an outer independent Roman dominating function (OIRDF) if the set of‎‎vertices assigned a 0 under f is an independent set‎. ‎The weight of an‎‎OIRDF is the sum of its function values over all vertices‎, ‎and the outer‎‎independent Roman domination number ΥoiR (G) is the minimum weight‎‎of an OIRDF on \$G\$‎. ‎In this paper‎, ‎we show that if T is a tree of order n ≥ 3 with s(T) support vertices‎, ‎then \$gamma _{oiR}(T)leq min‎ {%‎frac{5n}{6},frac{3n+s(T)}{4}}.\$ Moreover‎, ‎we characterize the tress‎‎attaining each bound‎.

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

## On trees with equal Roman domination and outer-independent Roman domination numbers

A Roman dominating function (RDF) on a graph \$G\$ is a function \$f : V (G) to {0, 1, 2}\$satisfying the condition that every vertex \$u\$ for which \$f(u) = 0\$ is adjacent to at least onevertex \$v\$ for which \$f(v) = 2\$. A Roman dominating function \$f\$ is called an outer-independentRoman dominating function (OIRDF) on \$G\$ if the set \${vin Vmid f(v)=0}\$ is independent.The (outer-independent) Roman dom...

متن کامل

## Bounds on the outer-independent double Italian domination number

An outer-independent double Italian dominating function (OIDIDF)on a graph \$G\$ with vertex set \$V(G)\$ is a function\$f:V(G)longrightarrow {0,1,2,3}\$ such that if \$f(v)in{0,1}\$ for a vertex \$vin V(G)\$ then \$sum_{uin N[v]}f(u)geq3\$,and the set \$ {uin V(G)|f(u)=0}\$ is independent. The weight ofan OIDIDF \$f\$ is the value \$w(f)=sum_{vin V(G)}f(v)\$. Theminimum weight of an OIDIDF on a graph \$G\$ is cal...

متن کامل

## Trees with strong equality between the Roman domination number and the unique response Roman domination number

A Roman dominating function (RDF) on a graph G = (V,E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of an RDF f is the value f(V (G)) = ∑ u∈V (G) f(u). A function f : V (G) → {0, 1, 2} with the ordered partition (V0, V1, V2) of V (G), where Vi = {v ∈ V (G) | f(v) = i} for i = 0...

متن کامل

## On trees with double domination number equal to 2-outer-independent domination number plus one

A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G = (V,E), a subset D ⊆ V (G) is a 2dominating set if every vertex of V (...

متن کامل

## Roman domination excellent graphs: trees

A Roman dominating function (RDF) on a graph \$G = (V, E)\$ is a labeling \$f : V rightarrow {0, 1, 2}\$ suchthat every vertex with label \$0\$ has a neighbor with label \$2\$. The weight of \$f\$ is the value \$f(V) = Sigma_{vin V} f(v)\$The Roman domination number, \$gamma_R(G)\$, of \$G\$ is theminimum weight of an RDF on \$G\$.An RDF of minimum weight is called a \$gamma_R\$-function.A graph G is said to be \$g...

متن کامل

## Co-Roman domination in trees

Abstract: Let G=(V,E) be a graph and let f:V(G)→{0,1,2} be a function‎. ‎A vertex v is protected with respect to f‎, ‎if f(v)>0 or f(v)=0 and v is adjacent to a vertex of positive weight‎. ‎The function f is a co-Roman dominating function‎, ‎abbreviated CRDF if‎: ‎(i) every vertex in V is protected‎, ‎and (ii) each u∈V with positive weight has a neighbor v∈V with f(v)=0 such that the func...

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 6  شماره 2

صفحات  273- 286

تاریخ انتشار 2021-12-01

{@ 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