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, 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.
Main Author: | Santhakumaran,A. P. |
---|---|
Format: | Digital revista |
Language: | English |
Published: |
Universidad Católica del Norte, Departamento de Matemáticas
2021
|
Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400963 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Similar Items
-
Edge-to-vertex m-detour monophonic number of a graph
by: Santhakumaran,A. P., et al.
Published: (2018) -
Edge Detour Monophonic Number of a Graph
by: Santhakumaran,A. P., et al.
Published: (2013) -
The forcing connected detour number of a graph
by: Santhakumaran,A. P., et al.
Published: (2014) -
The total detour monophonic number of a graph
by: Santhakumaran,A. P., et al.
Published: (2017) -
Upper Edge Detour Monophonic Number of a Graph
by: Titus,P, et al.
Published: (2014)