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Geodetic graphs of diameter two

✍ Scribed by A. Blokhuis; A. E. Brouwer


Publisher
Springer
Year
1988
Tongue
English
Weight
365 KB
Volume
25
Category
Article
ISSN
0046-5755

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✦ 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.


πŸ“œ SIMILAR VOLUMES


The structure of geodetic blocks with di
✍ Mao Jingzhong πŸ“‚ Article πŸ“… 1992 πŸ› John Wiley and Sons 🌐 English βš– 426 KB

## 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.

Reduced graphs of diameter two
✍ Hong-Jian Lai πŸ“‚ Article πŸ“… 1990 πŸ› John Wiley and Sons 🌐 English βš– 444 KB

## Abstract A graph __H__ is __collapsible__ if for every subset X βŠ† __V(H), H__ has a spanning connected subgraph whose set of odd‐degree 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

Erratum to: The structure of geodetic bl
✍ Mao Jingzhong; Sun Lingli πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 38 KB

## 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 : 79–80, 2004

Geodetic metrizations of graphs
✍ Frank Rhodes; Robert A. Melter πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 665 KB

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

Maximal planar graphs of diameter two
✍ Karen Seyffarth πŸ“‚ Article πŸ“… 1989 πŸ› John Wiley and Sons 🌐 English βš– 1020 KB

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.