Template:Graph families defined by their automorphisms
Revision as of 12:39, 17 August 2015 by imported>Maproom (replaced "t-transitive" by "n-transitive". On my system, the "t-" was displayed on a line by itself, and looked like a bit of fly-shit. "n" is a more substantial letter.)
| Graph families defined by their automorphisms | ||||
| distance-transitive | <math>\boldsymbol{\rightarrow}</math> | distance-regular | <math>\boldsymbol{\leftarrow}</math> | strongly regular |
| <math>\boldsymbol{\downarrow}</math> | ||||
| symmetric (arc-transitive) | <math>\boldsymbol{\leftarrow}</math> | n-transitive, n ≥ 2 | skew-symmetric | |
| <math>\boldsymbol{\downarrow}</math> | ||||
| (if connected) vertex- and edge-transitive | <math>\boldsymbol{\rightarrow}</math> | edge-transitive and regular | <math>\boldsymbol{\rightarrow}</math> | edge-transitive |
| <math>\boldsymbol{\downarrow}</math> | <math>\boldsymbol{\downarrow}</math> | <math>\boldsymbol{\downarrow}</math> | ||
| vertex-transitive | <math>\boldsymbol{\rightarrow}</math> | regular | <math>\boldsymbol{\rightarrow}</math> | (if bipartite) biregular |
| <math>\boldsymbol{\uparrow}</math> | ||||
| Cayley graph | <math>\boldsymbol{\leftarrow}</math> | zero-symmetric | asymmetric | |