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math.CO2022
On the Connectivity and Diameter of Geodetic Graphs
Asaf Etgar, Nati Linial
A graph 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…
math.CO2022
The -Rank and Size of Graphs
Gal Beniamini, Asaf Etgar, Yael Kirkpatrick
We consider the extremal family of graphs of order in which no two vertices have identical neighbourhoods, yet the adjacency matrix has rank only over the field of two el…