In the mathematical

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 field of graph theory

Graph theory

In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...

, the Balaban 11-cage or Balaban (3-11)-cage is a 3-regular graph

Regular graph

In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each vertex are equal to each other...

 with 112 vertices and 168 edges named after A. T. Balaban.

The Balaban 11-cage is the unique (3-11)-cage. It was discovered by Balaban in 1973. The unicity was proved by McKay and Myrvold in 2003.

The Balaban 11-cage is a Hamiltonian graph and can be constructed by excision from the Tutte 12-cage

Tutte 12-cage

In the mathematical field of graph theory, the Tutte 12-cage or Benson graph is a 3-regular graph with 126 vertices and 189 edges named after W. T. Tutte....

 by removing a small subtree and suppressing the resulting vertices of degree two.

It has chromatic number 3, chromatic index 3, radius 6, diameter 8 and girth 11. It is also a 3-vertex-connected graph

K-vertex-connected graph

In graph theory, a graph G with vertex set V is said to be k-vertex-connected if the graph remains connected when you delete fewer than k vertices from the graph...

 and a 3-edge-connected graph

K-edge-connected graph

In graph theory, a graph is k-edge-connected if it remains connected whenever fewer than k edges are removed.-Formal definition:Let G =  be an arbitrary graph....

.

Algebraic properties

The characteristic polynomial

Characteristic polynomial

In linear algebra, one associates a polynomial to every square matrix: its characteristic polynomial. This polynomial encodes several important properties of the matrix, most notably its eigenvalues, its determinant and its trace....

of the Balaban 11-cage is :
.

The automorphism group of the Balaban 11-cage is of order 64.