The Gavirtz graph is a strongly regular graph with 56 vertices and valency 10. The graph is named after the mathematician Allan Gavirtz, who described the graph in his dissertation [1] .
| Count of Gavirtz | |
|---|---|
 Some attachments with 7-fold symmetry. 8x or 14x symmetries impossible | |
| Named after | Allan Gavierz |
| Top | 56 |
| Riber | 280 |
| Diameter | 2 |
| Girth | four |
| Automorphisms | 80640 |
| Chromatic number | four |
| The properties | Very regular Hamilton No triangles Vertex-transitive Rib-transitive Remote Transitive |
Content
- 1 Construction
- 2 Properties
- 3 notes
- 4 Literature
Build
The Gavirtz graph can be constructed as follows. Consider the only Steiner system with 22 elements and 77 blocks. We choose an arbitrary element and consider the vertices of 56 blocks not associated with this element. We connect two blocks with an edge if they do not intersect.
According to this construction, one can embed the Gevirtz graph in the Higman – Sims graph .
Properties
The characteristic polynomial of the graph of Gevirtz is
Therefore, a graph is a whole graph — a graph whose spectrum consists entirely of integers. Count Gavirtz is fully defined by its spectrum.
The graph independence number is 16.
Notes
- ↑ Allan Gewirtz. Graphs with Maximal Even Girth . - City University of New York, 1967. - (Ph.D. Dissertation in Mathematics).
Literature
- Brouwer, Andries. Sims-Gewirtz graph .
- Weisstein, Eric W. Gewirtz graph on Wolfram MathWorld .