Harries–Wong graph
| Harries–Wong graph | |
|---|---|
 The Harries–Wong graph | |
| Named after | W. Harries, Pak-Ken Wong |
| Vertices | 70 |
| Edges | 105 |
| Radius | 6 |
| Diameter | 6 |
| Girth | 10 |
| Automorphisms | 24 (S4) |
| Chromatic number | 2 |
| Chromatic index | 3 |
| Book thickness | 3 |
| Queue number | 2 |
| Properties | Cubic Cage Triangle-free Hamiltonian |
| Table of graphs and parameters | |
In the mathematical field of graph theory, the Harries–Wong graph is a 3-regular undirected graph with 70 vertices and 105 edges.[1]
The Harries–Wong graph has chromatic number 2, chromatic index 3, radius 6, diameter 6, girth 10 and is Hamiltonian. It is also a 3-vertex-connected and 3-edge-connected non-planar cubic graph. It has book thickness 3 and queue number 2.[2]
The characteristic polynomial of the Harries–Wong graph is
History
In 1972, A. T. Balaban published a (3-10)-cage graph, a cubic graph that has as few vertices as possible for girth 10.[3] It was the first (3-10)-cage discovered but it was not unique.[4]
The complete list of (3-10)-cages and the proof of minimality was given by O'Keefe and Wong in 1980.[5] There exist three distinct (3-10)-cage graphs—the Balaban 10-cage, the Harries graph and the Harries–Wong graph.[6] Moreover, the Harries–Wong graph and Harries graph are cospectral graphs.
Gallery
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The chromatic number of the Harries–Wong graph is 2. -
The chromatic index of the Harries–Wong graph is 3. -
Alternative drawing of the Harries–Wong graph. -
The 8 orbits of the Harries–Wong graph.
References
- ^ Weisstein, Eric W. "Harries–Wong Graph". MathWorld.
- ^ Jessica Wolz, Engineering Linear Layouts with SAT. Master Thesis, University of Tübingen, 2018
- ^ A. T. Balaban, A trivalent graph of girth ten, J. Combin. Theory Ser. B 12, 1–5. 1972.
- ^ Pisanski, T.; Boben, M.; Marušič, D.; and Orbanić, A. "The Generalized Balaban Configurations." Preprint. 2001. [1].
- ^ M. O'Keefe and P.K. Wong, A smallest graph of girth 10 and valency 3, J. Combin. Theory Ser. B 29 (1980) 91–105.
- ^ Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 237, 1976.