Results 91 to 100 of about 1,279 (174)

Varieties of Roman domination IV

AKCE International Journal of Graphs and Combinatorics
Roman domination was introduced in 2004 by Cockayne, Dreyer, Hedetniemi, and Hedetniemi. If [Formula: see text] is the vertex set of a graph G, then a function [Formula: see text] is a Roman dominating function if every vertex [Formula: see text] for ...
M. Chellali, N. Jafari Rad, S.M. Sheikholeslami, L. Volkmann   +3 more
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Graphs with Large Hop Roman Domination Number [PDF]

Computer Science Journal of Moldova, 2019
A subset $S$ of vertices of a graph $G$ is a hop dominating set if every vertex outside $S$ is at distance two from a vertex of $S$. A Roman dominating function on a graph $G=(V,E)$ is a function $f: V(G) \longrightarrow \{0, 1, 2\}$ satisfying the ...
E. Shabani, N. Jafari Rad, A. Poureidi
doaj  

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 ...
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Outer-clique Roman dominating function in graphs

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.
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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
openaire   +1 more source

Perfect Roman and Perfect Italian Domination of Cartesian Product Graphs

Scientific Journal of King Faisal University: Basic and Applied Sciences
For a graph G=(V,E), a function f:V→{0,1,2} is a perfect Roman dominating function (PRDF) on G if every v∈V with f(v)=0 is adjacent to exactly one vertex u with f(u)=2. The sum ∑_(v∈V)^▒f (v) is the weight w(f) of f.
Ahlam Almulhim
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A note on k-Roman graphs [PDF]

Tyt. z nagłówka.Bibliogr. s. 646.Let G = (V,E) be a graph and let k be a positive integer. A subset D of V (G) is a k-dominating set of G if every vertex in [formula] has at least k neighbours in D.
Bouchou, Ahmed.
core  

Roman domination on graphs [PDF]

, 2010
A Roman dominating function of a graph G is a function f : V (G) → {0, 1, 2} such that whenever f(v) = 0 there xists a vertex u adjacent to v such that f(u) = 2. The weight of f is w(f) = Pv∈V (G) f(v).
劉俊宏, Liu, Chun-Hung
core  

Co-Roman dominating of girds

پژوهش‌های ریاضی, 2022
Rana Khoeilr, marzieh soroudi, Maryam Atapour   +2 more
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Novel Roman domination-based graph energies for QSPR analysis of neuroprotective herbal compounds in Alzheimer's disease treatment. [PDF]

Front Chem
Salini Jancy Rani A, Balamurugan BJ.
europepmc   +1 more source