Results 11 to 20 of about 1,370 (272)
Unique response strong Roman dominating functions of graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2021 Given a simple graph G=(V,E) with maximum degree Δ. Let (V0, V1, V2) be an ordered partition of V, where Vi = {v ∈ V : f(v)=i} for i = 0, 1 and V2 = {v ∈ V : f(v)≥2}.
Doost Ali Mojdeh +3 more
doaj +2 more sources
Roman Census: Enumerating and Counting Roman Dominating Functions on Graph Classes [PDF]
, 2023 The concept of Roman domination has recently been studied concerning enumerating and counting in F. N. Abu-Khzam et al. (WG 2022). More technically speaking, a function that assigns 0,1,2 to the vertices of an undirected graph is called a Roman ...
Abu-Khzam, Faisal N. +2 more
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Restrained condition on double Roman dominating functions
Applied Mathematics and Computation, 2022 We continue the study of restrained double Roman domination in graphs. For a graph $G=\big{(}V(G),E(G)\big{)}$, a double Roman dominating function $f$ is called a restrained double Roman dominating function (RDRD function) if the subgraph induced by $\{v\
Samadi, Babak +12 more
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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=
Casinillo, Leomarich F
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Smarandachely Roman Edge s-dominating Function
, 2010 For an integer n ≥ 2, let I ⊂ {0, 1, 2, · · · , n}. A Smarandachely Roman s-dominating function for an integer s, 2 ≤ s ≤ n on a graph G = (V,E) is a function f: V → {0, 1,2, · · · , n} satisfying the condition that |f(u) − f(v) | ≥ s for each ...
L. Pushpalatha, Karam Ebadi
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Signed total double Roman dominating functions in graphs
AKCE International Journal of Graphs and CombinatoricsA signed total double Roman dominating function (STDRDF) on an isolated-free graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex v with [Formula: see text] has at least two neighbors assigned 2 under f or one neighbor w
H. Abdollahzadeh Ahangar +2 more
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Fair hop Roman dominating function in graphs [PDF]
Annals of Mathematics and Computer ScienceThis 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 ...
Casinillo, Leomarich
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Total Roman domination for proper interval graphs
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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Outer-connected fair Roman dominating function in graphs [PDF]
Annals of Mathematics and Computer ScienceIn this paper, we introduce and investigate a new variant of a Roman dominating function in graphs called outer-connected fair Roman dominating function.
Casinillo, Emily, Casinillo, Leomarich
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The Roman domatic number of a graph
Applied Mathematics Letters, 2010 A Roman dominating function on a graph G is a labeling f:V(G)⟶{0,1,2} such that every vertex with label 0 has a neighbor with label 2. A set {f1,f2,…,fd} of Roman dominating functions on G with the property that ∑i=1dfi(v)≤2 for each v∈V(G) is called a ...
S M Sheikholeslami, Lutz Volkmann
exaly +2 more sources