Results 11 to 20 of about 5,939,930 (166)

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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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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Smarandachely Roman Edge S-Dominating Function

, 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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Outer-clique Roman dominating function in graphs [PDF]

Annals of Mathematics and Computer Science
This paper introduces a new restricted variant of a Roman dominating function in graphs called the outer-clique Roman dominating function and discusses some graph-theoretic properties.
Casinillo, Leomarich
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Interior hop Roman dominating function in graphs

Annals of Communications in Mathematics
Let G = (V (G), E(G)) be a simple non-complete graph and let ξ : V → {0, 1, 2} be an HRDF on G. For each j ∈ {0, 1, 2}, let Vj = {x ∈ V (G) : ξ(x) = j}. Then ξ = (V0, V1, V2). A function ξ is an interior hop Roman dominating function (InHRDF) on G if for each v ∈ V0, there exists u ∈ V2 such that dG(u, v) = 2, and eitherV1 = V (G) or for every w ∈ V2 ...
Casinillo, Leomarich
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Outer-convex Hop Roman Dominating Function in Graphs

Annals of Communications in Mathematics
Let G = (V (G), E(G)) be a connected graph and let f : V (G) → {0, 1, 2} be a hop Roman dominating function (HRDF) on G. If for each k ∈ {0, 1, 2}, Vk = {x ∈ V (G) : f(x) = k}, then f = (V0, V1, V2). A function f is an outer-convex hop Roman dominating function (OConHRDF) on G provided that for every v ∈ V0, there exists u ∈ V2 such that v ∈ N2G(u) and
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
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On Double Roman Dominating Functions in Graphs

European Journal of Pure and Applied Mathematics, 2023
Let G be a connected graph. A function f : V (G) → {0, 1, 2, 3} is a double Roman dominating function of G if for each v ∈ V (G) with f(v) = 0, v has two adjacent vertices u and w for which f(u) = f(w) = 2 or v has an adjacent vertex u for which f(u) = 3, and for each v ∈ V (G) with f(v) = 1, v is adjacent to a vertex u for which either f(u) = 2 or f(u)
Jerry Boy Cariaga, Ferdinand Jamil
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A Constructive Characterization of Vertex Cover Roman Trees

Discussiones Mathematicae Graph Theory, 2021
A Roman dominating function on a graph G = (V (G), E(G)) is a function f : V (G) → {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.
Martínez Abel Cabrera, Kuziak Dorota, Yero Ismael G.   +2 more
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Geodetic Roman Dominating Functions in a Graph

European Journal of Pure and Applied Mathematics, 2023
Let $G$ be a connected graph. A function $f: V(G)\rightarrow \{0,1,2\}$ is a \textit{geodetic Roman dominating function} (or GRDF) if every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$ and $V_1 \cup V_2$ is a geodetic set in $G$.
Rona Jane Gamayot Fortosa, Sergio Canoy
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