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| Articolul urmator |
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 696 6 |
| Ultima descărcare din IBN: 2023-04-01 01:34 |
| Căutarea după subiecte similare conform CZU |
| 519.17 (68) |
| Analiză combinatorică. Teoria grafurilor (115) |
 SM ISO690:2012SHABANI, 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 |
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| Numărul 1(79) / 2019 / ISSN 1561-4042 /ISSNe 2587-4330 | ||||||
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| CZU: 519.17 | ||||||
| MSC 2010: 2010. 05C69 | ||||||
| Pag. 3-22 | ||||||
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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. |
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| Cuvinte-cheie Domination, Roman domination, Hop Roman domination |
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<title xml:lang='en'>Graphs with Large Hop Roman Domination Number</title>
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<subject>Domination</subject>
<subject>Roman domination</subject>
<subject>Hop Roman
domination</subject>
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<description xml:lang='en' descriptionType='Abstract'><p>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.</p></description>
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