Graphs of edge-to-vertex detour number 2
Abstract 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,...
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Universidad Católica del Norte, Departamento de Matemáticas
2021
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oai:scielo:S0716-091720210004009632021-08-12Graphs of edge-to-vertex detour number 2Santhakumaran,A. P. Detour Edge-to-vertex detour set Edge-to-vertex detour basis Edge-to-vertex detour number Abstract 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 some 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 dn 2 (G) of G is the minimum order of its edge-to-vertex detour sets and any edge-to-vertex detour set of order dn 2 (G) is an edge-to-vertex detour basis of G. Graphs G of size q for which dn 2 (G)=2 are characterized.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.40 n.4 20212021-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400963en10.22199/issn.0717-6279-4454 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Detour Edge-to-vertex detour set Edge-to-vertex detour basis Edge-to-vertex detour number |
| spellingShingle |
Detour Edge-to-vertex detour set Edge-to-vertex detour basis Edge-to-vertex detour number Santhakumaran,A. P. Graphs of edge-to-vertex detour number 2 |
| description |
Abstract 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 some 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 dn 2 (G) of G is the minimum order of its edge-to-vertex detour sets and any edge-to-vertex detour set of order dn 2 (G) is an edge-to-vertex detour basis of G. Graphs G of size q for which dn 2 (G)=2 are characterized. |
| author |
Santhakumaran,A. P. |
| author_facet |
Santhakumaran,A. P. |
| author_sort |
Santhakumaran,A. P. |
| title |
Graphs of edge-to-vertex detour number 2 |
| title_short |
Graphs of edge-to-vertex detour number 2 |
| title_full |
Graphs of edge-to-vertex detour number 2 |
| title_fullStr |
Graphs of edge-to-vertex detour number 2 |
| title_full_unstemmed |
Graphs of edge-to-vertex detour number 2 |
| title_sort |
graphs of edge-to-vertex detour number 2 |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2021 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400963 |
| work_keys_str_mv |
AT santhakumaranap graphsofedgetovertexdetournumber2 |
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1718439911668842496 |