The upper edge-to-vertex detour number of a graph
For two vertices u and v in a graph G = (V, E), the detour distance D(u, v) is the length of a longest u-v path in G. A u-v path of length D(u, v) is called a u-v detour. For subsets A and B of V, the detour distance D(A, B) is defined as D(A, B) = min{D(x, y): x ∈ A, y ∈ B}. A u-v path of length D(...
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| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2012
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/152187 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The upper edge-to-vertex detour number of a graph / A.P. Santhakumaran, S. Athisayanathan // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 128–138. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1521872019-06-09T01:25:13Z The upper edge-to-vertex detour number of a graph Santhakumaran, A.P. Athisayanathan, S. For two vertices u and v in a graph G = (V, E), the detour distance D(u, v) is the length of a longest u-v path in G. A u-v path of length D(u, v) is called a u-v detour. For subsets A and B of V, the detour distance D(A, B) is defined as D(A, B) = min{D(x, y): x ∈ A, y ∈ B}. A u-v path of length D(A, B) is called an A-B detour joining the sets A, B ⊆ V where u ∈ A and v ∈ B. A vertex x is said to lie on an A-B detour if x is a vertex of an A-B detour. A set S ⊆ E is called an edge-to-vertex detour set if every vertex of G is incident with an edge of S or lies on a detour joining a pair of edges of S. The edge-to-vertex detour number dn₂(G) of G is the minimum order of its edge-to-vertex detour sets and any edge-to-vertex detour set of order dn₂(G) is an edge-to-vertex detour basis of G. An edge-to-vertex detour set S in a connected graph G is called a minimal edge-to-vertex detour set of G if no proper subset of S is an edge-to-vertex detour set of G. The upper edge-to-vertex detour number, dn₂⁺(G) of G is the maximum cardinality of a minimal edge-to-vertex detour set of G. The upper edge-to-vertex detour numbers of certain standard graphs are obtained. It is shown that for every pair a, b of integers with 2 ≤ a ≤ b, there exists a connected graph G with dn2(G) = a and dn₂⁺(G) = b. 2012 Article The upper edge-to-vertex detour number of a graph / A.P. Santhakumaran, S. Athisayanathan // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 128–138. — Бібліогр.: 9 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:05C12. http://dspace.nbuv.gov.ua/handle/123456789/152187 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
For two vertices u and v in a graph G = (V, E), the detour distance D(u, v) is the length of a longest u-v path in G. A u-v path of length D(u, v) is called a u-v detour. For subsets A and B of V, the detour distance D(A, B) is defined as D(A, B) = min{D(x, y): x ∈ A, y ∈ B}. A u-v path of length D(A, B) is called an A-B detour joining the sets A, B ⊆ V where u ∈ A and v ∈ B. A vertex x is said to lie on an A-B detour if x is a vertex of an A-B detour. A set S ⊆ E is called an edge-to-vertex detour set if every vertex of G is incident with an edge of S or lies on a detour joining a pair of edges of S. The edge-to-vertex detour number dn₂(G) of G is the minimum order of its edge-to-vertex detour sets and any edge-to-vertex detour set of order dn₂(G) is an edge-to-vertex detour basis of G. An edge-to-vertex detour set S in a connected graph G is called a minimal edge-to-vertex detour set of G if no proper subset of S is an edge-to-vertex detour set of G. The upper edge-to-vertex detour number, dn₂⁺(G) of G is the maximum cardinality of a minimal edge-to-vertex detour set of G. The upper edge-to-vertex detour numbers of certain standard graphs are obtained. It is shown that for every pair a, b of integers with 2 ≤ a ≤ b, there exists a connected graph G with dn2(G) = a and dn₂⁺(G) = b. |
| format |
Article |
| author |
Santhakumaran, A.P. Athisayanathan, S. |
| spellingShingle |
Santhakumaran, A.P. Athisayanathan, S. The upper edge-to-vertex detour number of a graph Algebra and Discrete Mathematics |
| author_facet |
Santhakumaran, A.P. Athisayanathan, S. |
| author_sort |
Santhakumaran, A.P. |
| title |
The upper edge-to-vertex detour number of a graph |
| title_short |
The upper edge-to-vertex detour number of a graph |
| title_full |
The upper edge-to-vertex detour number of a graph |
| title_fullStr |
The upper edge-to-vertex detour number of a graph |
| title_full_unstemmed |
The upper edge-to-vertex detour number of a graph |
| title_sort |
upper edge-to-vertex detour number of a graph |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152187 |
| citation_txt |
The upper edge-to-vertex detour number of a graph / A.P. Santhakumaran, S. Athisayanathan // Algebra and Discrete Mathematics. — 2012. — Vol. 13, № 1. — С. 128–138. — Бібліогр.: 9 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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