On the connectivity and diameter of geodetic graphs

Asaf Etgar, Nati Linial

Research output: Contribution to journalArticlepeer-review

Abstract

A graph G is geodetic if between any two vertices there exists a unique shortest path. In 1962 Ore raised the challenge to characterize geodetic graphs, but despite many attempts, such characterization still seems well beyond reach. We may assume, of course, that G is 2-connected, and here we consider only graphs with no vertices of degree 1 or 2. We prove that all such graphs are, in fact 3-connected. We also construct an infinite family of such graphs of the largest known diameter, namely 5.

Original languageAmerican English
Article number103886
JournalEuropean Journal of Combinatorics
Volume116
DOIs
StatePublished - Feb 2024

Bibliographical note

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© 2023 Elsevier Ltd

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