Locally linear graph: Difference between revisions

Revision as of 07:25, 5 August 2021

Revision as of 07:26, 5 August 2021

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==Constructions==

===Gluing and products===

[[File:Friendship graphs.svg|thumb|[[Friendship graph]]s]]

The [[friendship graph]]s, graphs formed by gluing together a collection of triangles at a single shared vertex, are locally linear. They are the only finite graphs having the stronger property that every pair of vertices (adjacent or not) share exactly one common neighbor.{{r|ers}} More generally every [[Cactus graph#Triangular cactus|triangular cactus graph]], a graph formed by gluing triangles at shared vertices without forming any additional cycles, is locally linear.{{r|fp}}