Geodetic graphs of diameter two
β Scribed by A. Blokhuis; A. E. Brouwer
- Publisher
- Springer
- Year
- 1988
- Tongue
- English
- Weight
- 365 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0046-5755
No coin nor oath required. For personal study only.
β¦ Synopsis
We survey what is known on geodetic graphs of diameter two and discuss the implications of a new strong necessary condition for the existence of such graphs.
π SIMILAR VOLUMES
## Abstract In this paper we prove that all geodetic blocks of diameter two can be divided in four types, i.e., Moore graphs with diameter two, regular pyramids with altitude 2, type AP and type PP. We also give the answers to the questions posed by J. G. Stemple in 1974.
## Abstract A graph __H__ is __collapsible__ if for every subset X β __V(H), H__ has a spanning connected subgraph whose set of oddβdegree vertices is X. In any graph __G__ there is a unique collection of maximal collapsible subgraphs, and when all of them are contracted, the resulting contraction
## Abstract In our paper 1 we gave a classification of geodetic blocks of diameter two, but the proof was incorrect. Here we point out this error and give a new result about constructing geodetic blocks of diameter two. Β© 2004 Wiley Periodicals, Inc. J Graph Theory 46 : 79β80, 2004
A graph can be metrized by assigning a length to each of its edges. Such a graph is said to be geodetic if for each pair of vertices there is a unique geodesic joining them. It is said to be normally geodetic if each of these unique geodesics is one of the geodesics in the usual metrization of the g
A maximal planar graph is a simple planar graph in which every face is a triangle. We show here that such graphs with maximum degree A and diameter two have no more than :A + 1 vertices. We also show that there exist maximal planar graphs with diameter two and exactly LiA + 1 J vertices.