Graphs with Large Hop Roman Domination Number

Shabani E.; Nader Jafari Rad; Poureidi A.

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694

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2023-04-01 01:34

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similare conform CZU

519.17 (68)

Analiză combinatorică. Teoria grafurilor (115)

SM ISO690:2012

SHABANI, E., NADER JAFARI, Rad, POUREIDI, A.. Graphs with Large Hop Roman Domination Number. In: Computer Science Journal of Moldova, 2019, nr. 1(79), pp. 3-22. ISSN 1561-4042.

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Computer Science Journal of Moldova

Numărul 1(79) / 2019 / ISSN 1561-4042 /ISSNe 2587-4330

Graphs with Large Hop Roman Domination Number

CZU: 519.17

MSC 2010: 2010. 05C69

Pag. 3-22

Shabani E., Nader Jafari Rad, Poureidi A.

University of Technology Shahrood

Disponibil în IBN: 30 mai 2019

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Rezumat

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) −→ {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. A hop Roman dominating function (HRDF) of G is a function f : V (G) −→ {0, 1, 2} having the property that for every vertex v ∈ V with f(v) = 0 there is a vertex u with f(u) = 2 and d(u, v) = 2. The weight of a HRDF f is the sum f(V ) = ∑ Pv2V f(v). The minimum weight of a HRDF on G is called the hop Roman domination number of G and is denoted by hR(G). In this paper we characterize all graphs G of order n with hR(G) = n or hR(G) = n − 1.

Cuvinte-cheie
Domination, Roman domination, Hop Roman domination

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