In graph theory, the Harris – Wong graph is a 3-regular undirected graph with 70 vertices and 105 edges [1] .
| Earl of Harris - Wong | |
|---|---|
 | |
| Top | 70 |
| Riber | 105 |
| Radius | 6 |
| Diameter | 6 |
| Girth | ten |
| Automorphisms | 24 ( S 4 ) |
| Chromatic number | 2 |
| Chromatic Index | 3 |
| The properties | cubic cell no triangles hamilton |
The chromatic number of the graph is 2, the chromatic index is 3, the diameter of the graph and radius are 6, and the girth is 10.
The graph is a Hamiltonian , vertex 3-connected , edge-3-connected , planar cubic graph.
The characteristic polynomial of Count Harris - Wong is
History
In 1972, AT Balaban (3–10) published a cell , a cubic graph that has a minimum number of vertices for a girth of 10 [2] . It was the first open (3-10) -cell, but it is not unique [3] .
A complete list of (3-10) -cells and proof of minimality were given by O'Keefe and Wong in 1980 [4] . There are only three different (3-10) -cells - the , Earl of Harris and Earl of Harris - Wong [5] . Moreover, the Harris-Wong count and the Harris count are cospectral graphs .
Gallery
The chromatic number of Earl Harris-Wong is 2.
The Harris - Wong graph chromatic index is 3.
An alternative drawing of Earl Harris - Wong.
8 orbits of Earl Harris - Wong.
Notes
- ↑ Weisstein, Eric W. Harries – Wong Graph on Wolfram MathWorld .
- ↑ Balaban, 1972 , p. 1-5.
- ↑ Pisanski, Boben, Marušič, Orbanić, 2001 .
- ↑ O'Keefe, Wong, 1980 , p. 91-105.
- ↑ Bondy, Murty, 1976 , p. 237.
Literature
- AT Balaban. A trivalent graph of girth ten // J. Combin. Theory Ser. B. - 1972. - Vol. 12 . - S. 1-5 .
- T. Pisanski, M. Boben, D. Marušič, A. Orbanić. The Generalized Balaban Configurations // Preprint. - 2001.
- M. O'Keefe, PK Wong. A smallest graph of girth 10 and valency 3 // J. Combin. Theory Ser. B. - 1980. - Vol. 29 .
- JA Bondy, USR Murty. Graph Theory with Applications. - New York: North Holland, 1976 .-- S. 237.