TY - JOUR
T1 - On the connectivity and diameter of geodetic graphs
AU - Etgar, Asaf
AU - Linial, Nati
N1 - Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2024/2
Y1 - 2024/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85177222529&partnerID=8YFLogxK
U2 - 10.1016/j.ejc.2023.103886
DO - 10.1016/j.ejc.2023.103886
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AN - SCOPUS:85177222529
SN - 0195-6698
VL - 116
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
M1 - 103886
ER -