Balaban 10-cage | |
---|---|
Named after | Alexandru T. Balaban |
Vertices | 70 |
Edges | 105 |
Radius | 6 |
Diameter | 6 |
Girth | 10 |
Automorphisms | 80 |
Chromatic number | 2 |
Chromatic index | 3 |
Genus | 9 |
Book thickness | 3 |
Queue number | 2 |
Properties |
Cubic Cage Hamiltonian |
Table of graphs and parameters |
In the mathematical field of graph theory, the Balaban 10-cage or Balaban (3,10)-cage is a 3- regular graph with 70 vertices and 105 edges named after Alexandru T. Balaban. [1] Published in 1972, [2] It was the first 10- cage discovered but it is not unique. [3]
The complete list of 10-cages and the proof of minimality was given by Mary R. O'Keefe and Pak Ken Wong. [4] There exist 3 distinct (3,10)-cages, the other two being the Harries graph and the Harries–Wong graph. [5] Moreover, the Harries–Wong graph and Harries graph are cospectral graphs.
The Balaban 10-cage has chromatic number 2, chromatic index 3, diameter 6, girth 10 and is hamiltonian. It is also a 3- vertex-connected graph and 3- edge-connected. The book thickness is 3 and the queue number is 2. [6]
The characteristic polynomial of the Balaban 10-cage is
Molecular graph
Balaban 11-cage
Balaban 10-cage | |
---|---|
Named after | Alexandru T. Balaban |
Vertices | 70 |
Edges | 105 |
Radius | 6 |
Diameter | 6 |
Girth | 10 |
Automorphisms | 80 |
Chromatic number | 2 |
Chromatic index | 3 |
Genus | 9 |
Book thickness | 3 |
Queue number | 2 |
Properties |
Cubic Cage Hamiltonian |
Table of graphs and parameters |
In the mathematical field of graph theory, the Balaban 10-cage or Balaban (3,10)-cage is a 3- regular graph with 70 vertices and 105 edges named after Alexandru T. Balaban. [1] Published in 1972, [2] It was the first 10- cage discovered but it is not unique. [3]
The complete list of 10-cages and the proof of minimality was given by Mary R. O'Keefe and Pak Ken Wong. [4] There exist 3 distinct (3,10)-cages, the other two being the Harries graph and the Harries–Wong graph. [5] Moreover, the Harries–Wong graph and Harries graph are cospectral graphs.
The Balaban 10-cage has chromatic number 2, chromatic index 3, diameter 6, girth 10 and is hamiltonian. It is also a 3- vertex-connected graph and 3- edge-connected. The book thickness is 3 and the queue number is 2. [6]
The characteristic polynomial of the Balaban 10-cage is
Molecular graph
Balaban 11-cage