On geodetic sets formed by boundary vertices
Visualitza/Obre
Tipus de documentArticle
Data publicació2003
Condicions d'accésAccés obert
Llevat que s'hi indiqui el contrari, els
continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
:
Reconeixement-NoComercial-SenseObraDerivada 2.5 Espanya
Abstract
Let G be a finite simple connected graph. A vertex v is a boundary vertex of G if
there exists a vertex u such that no neighbor of v is further away from u than v.
We obtain a number of properties involving different types of boundary vertices:
peripheral, contour and eccentric vertices. Before showing that one of the main
results in [3] does not hold for one of the cases, we establish a realization theorem
that not only corrects the mentioned wrong statement but also improves it.
Given S ⊆ V (G), its geodetic closure I[S] is the set of all vertices lying on some
shortest path joining two vertices of S. We prove that the boundary vertex set
∂(G) of any graph G is geodetic, that is, I[∂(G)] = V (G). A vertex v belongs to
the contour Ct(G) of G if no neighbor of v has an eccentricity greater than v. We
present some sufficient conditions to guarantee the geodeticity of either the contour
Ct(G) or its geodetic closure I[Ct(G)].
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
030403hernando.ps | 192,1Kb | Postscript | Visualitza/Obre |