Английская Википедия:Balaban 11-cage
Шаблон:Infobox graph In the mathematical field of graph theory, the Balaban 11-cage or Balaban (3,11)-cage is a 3-regular graph with 112 vertices and 168 edges named after Alexandru T. Balaban.[1]
The Balaban 11-cage is the unique (3,11)-cage. It was discovered by Balaban in 1973.[2] The uniqueness was proved by Brendan McKay and Wendy Myrvold in 2003.[3]
The Balaban 11-cage is a Hamiltonian graph and can be constructed by excision from the Tutte 12-cage by removing a small subtree and suppressing the resulting vertices of degree two.[4]
It has independence number 52,[5] chromatic number 3, chromatic index 3, radius 6, diameter 8 and girth 11. It is also a 3-vertex-connected graph and a 3-edge-connected graph.
The characteristic polynomial of the Balaban 11-cage is:
- <math>(x-3) x^{12} (x^2-6)^5 (x^2-2)^{12} (x^3-x^2-4 x+2)^2\cdot</math>
- <math>\cdot(x^3+x^2-6 x-2) (x^4-x^3-6 x^2+4 x+4)^4 \cdot</math>
- <math>\cdot(x^5+x^4-8 x^3-6 x^2+12 x+4)^8</math>.
The automorphism group of the Balaban 11-cage is of order 64.[4]
Gallery
-
The chromatic number of the Balaban 11-cage is 3.
-
The chromatic index of the Balaban 11-cage is 3.
-
Alternative drawing of the Balaban 11-cage.[6]
References
References
- ↑ Шаблон:MathWorld
- ↑ Balaban, Alexandru T., Trivalent graphs of girth nine and eleven, and relationships among cages, Revue Roumaine de Mathématiques Pures et Appliquées 18 (1973), 1033-1043. Шаблон:MR
- ↑ Шаблон:MathWorld
- ↑ 4,0 4,1 Geoffrey Exoo & Robert Jajcay, Dynamic cage survey, Electr. J. Combin. 15 (2008)
- ↑ Шаблон:Harvtxt
- ↑ P. Eades, J. Marks, P. Mutzel, S. North. "Graph-Drawing Contest Report", TR98-16, December 1998, Mitsubishi Electric Research Laboratories.
![Alternative drawing of the Balaban 11-cage.[6]](/ruwiki/index.php?title=%D0%A1%D0%BB%D1%83%D0%B6%D0%B5%D0%B1%D0%BD%D0%B0%D1%8F:%D0%97%D0%B0%D0%B3%D1%80%D1%83%D0%B7%D0%BA%D0%B0&wpDestFile=Balaban_11-cage_alternative_drawing.svg){kind=link}