Feb '26 Notes
By Susam Pal on 27 Feb 2026 [draft]
The usual monthly notes.
Contents
- Regular Non-Vertex-Transitive Graphs
- Vertex Transitive But Not Edge Transitive
- Edge Transitive But Not Vertex Transitive
Regular Non-Vertex-Transitive Graphs
The Frucht graph and the Folkman graph are examples of graphs that are \( k \)-regular but not vertex transitive. In fact, the Folkman graph is a semi-symmetric graph, i.e. it is regular and edge-transitive but not vertex-transitive.
Vertex Transitive But Not Edge Transitive
The circular ladder graph \( CL_3, \) i.e. the triangualr prism graph, is vertex transitive but not edge transitive.
Edge Transitive But Not Vertex Transitive
The complete bipartite graphs \( K_{m,n} \) with \( m \ne n \) are edge transitive but not vertex transitive.