| Conţinutul numărului revistei |
| Articolul precedent |
| Articolul urmator |
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 SM ISO690:2012KAMALIAN, Rafayel. On cyclically-interval edge colorings of trees. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2012, nr. 1(68), pp. 50-58. ISSN 1024-7696. |
| EXPORT metadate: Google Scholar Crossref CERIF DataCite Dublin Core |
 Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica |
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| Numărul 1(68) / 2012 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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| Pag. 50-58 | ||||||
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For an undirected, simple, finite, connected graph G, we denote by V (G)
and E(G) the sets of its vertices and edges, respectively. A function ' : E(G) →
{1, 2, . . . , t} is called a proper edge t-coloring of a graph G if adjacent edges are
colored differently and each of t colors is used. An arbitrary nonempty subset of
consecutive integers is called an interval. If ' is a proper edge t-coloring of a graph
G and x ∈ V (G), then SG(x, ') denotes the set of colors of edges of G which are
incident with x. A proper edge t-coloring ' of a graph G is called a cyclically-interval
t-coloring if for any x ∈ V (G) at least one of the following two conditions holds: a)
SG(x,') is an interval, b) {1, 2, . . . , t} \ SG(x, ') is an interval. For any t ∈ N, let
Mt be the set of graphs for which there exists a cyclically-interval t-coloring, and let
M ≡St≥1 Mt. For an arbitrary tree G, it is proved that G ∈ M and all possible
values of t are found for which G ∈ Mt. |
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| Cuvinte-cheie Tree, interval edge coloring, cyclically-interval edge coloring. |
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<title xml:lang='en'>On cyclically-interval edge colorings of trees</title>
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<publisher>Instrumentul Bibliometric National</publisher>
<publicationYear>2012</publicationYear>
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<subject>Tree</subject>
<subject>interval edge coloring</subject>
<subject>cyclically-interval edge
coloring.</subject>
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<date dateType='Issued'>2012-04-03</date>
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<description xml:lang='en' descriptionType='Abstract'>For an undirected, simple, finite, connected graph G, we denote by V (G)
and E(G) the sets of its vertices and edges, respectively. A function ' : E(G) →
{1, 2, . . . , t} is called a proper edge t-coloring of a graph G if adjacent edges are
colored differently and each of t colors is used. An arbitrary nonempty subset of
consecutive integers is called an interval. If ' is a proper edge t-coloring of a graph
G and x ∈ V (G), then SG(x, ') denotes the set of colors of edges of G which are
incident with x. A proper edge t-coloring ' of a graph G is called a cyclically-interval
t-coloring if for any x ∈ V (G) at least one of the following two conditions holds: a)
SG(x,') is an interval, b) {1, 2, . . . , t} \ SG(x, ') is an interval. For any t ∈ N, let
Mt be the set of graphs for which there exists a cyclically-interval t-coloring, and let
M ≡St≥1 Mt. For an arbitrary tree G, it is proved that G ∈ M and all possible
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