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 HarriesâWong graph is
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 graphsâthe Balaban 10-cage, the Harries graph and the Harries–Wong graph. [6] Moreover, the Harries–Wong graph and Harries graph are cospectral graphs.
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 HarriesâWong graph is
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 graphsâthe Balaban 10-cage, the Harries graph and the Harries–Wong graph. [6] Moreover, the Harries–Wong graph and Harries graph are cospectral graphs.