Results 11 to 20 of about 1,279 (174)

A note on the edge Roman domination in trees [PDF]

Electronic Journal of Graph Theory and Applications, 2017
A subset $X$ of edges of a graph $G$ is called an \textit{edgedominating set} of $G$ if every edge not in $X$ is adjacent tosome edge in $X$. The edge domination number $\gamma'(G)$ of $G$ is the minimum cardinality taken over all edge dominating sets of 
Nader Jafari Rad
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Fair Secure Roman Dominating Function in Graphs

InPrime
Let G=(V(G),E(G)) be a graph and let ϕ:V(G)→{0,1,2} be a function on G. For each i∈{0,1,2}, let V_i={v∈V(G):ϕ(v)=i}. Then ϕ can be represented as ϕ=(V_0,V_1,V_2).
Leomarich Casinillo, Emily L. Casinillo
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Smarandachely Roman Edge S-Dominating Function [PDF]

, 2010
In this paper, we find lower and upper bounds for Roman edge domination numbers in terms of the diameter and girth of G.
Ebadi, Karam, Pushpalatha, I.
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Double Roman domination and domatic numbers of graphs [PDF]

Communications in Combinatorics and Optimization, 2018
A double Roman dominating function on a graph $G$ with vertex set $V(G)$ is defined in \cite{bhh} as a function‎ ‎$f:V(G)\rightarrow\{0,1,2,3\}$ having the property that if $f(v)=0$‎, ‎then the vertex $v$ must have at least two‎ ‎neighbors assigned 2 ...
L. Volkmann
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Restrained roman domination in graphs [PDF]

Transactions on Combinatorics, 2015
A Roman dominating function (RDF) on a graph G = (V,E) is defined to be a function 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. A set S V is a Restrained dominating set if every
Roushini Leely Pushpam , Padmapriea Sampath   +1 more
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Outer-connected fair Roman dominating function in graphs [PDF]

Annals of Mathematics and Computer Science
In this paper, we introduce and investigate a new variant of a Roman dominating function in graphs called outer-connected fair Roman dominating function. In addition, we presented some theoretical properties of outer-connected fair Roman dominating functions in some classes of connected graphs and discussed some important results.
Leomarich Casinillo, null Emily Casinillo   +1 more
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Total Roman domination for proper interval graphs [PDF]

Electronic Journal of Graph Theory and Applications, 2020
A function f:V → {0,1,2} is a total Roman dominating function (TRDF) on a graph G=(V,E) if for every vertex v ∈ V with f(v) = 0 there is a vertex u adjacent to v with f(u) = 2 and for every vertex v ∈ V with f(v) > 0 there exists a vertex u ∈ NG(v ...
Abolfazl Poureidi
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Fair hop Roman dominating function in graphs [PDF]

Annals of Mathematics and Computer Science
This paper introduces a new variant of a hop Roman dominating function in graphs called the fair hop Roman dominating function. Moreover, several important combinatorial properties and characterizations of fair hop Roman dominating functions in various graph classes were investigated.
Casinillo, Leomarich
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A note on outer-connected hop Roman dominating function in graphs [PDF]

Journal of Fundamental Mathematics and Applications (JFMA)
Let $G=(V(G), E(G))$ be a simple, connected, and finite graph with vertex set $V(G)$ and edge set $E(G)$.  Let $\phi: V(G) \rightarrow \{0, 1, 2\}$  be an HRDF on $G$, and for each $i\in \{0, 1, 2\}$, let  $V_i=\{u\in V(G): \phi(u)=i\}$. A function $\phi=(V_0, V_1, V_2)$ is an outer-connected hop Roman dominating function (OcHRDF) on $G$ if, for every $
Casinillo, Leomarich F
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On The Roman Domination Stable Graphs [PDF]

Discussiones Mathematicae Graph Theory, 2017
A Roman dominating function (or just 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.
Hajian Majid, Rad Nader Jafari
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