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    Balaban 10-cage

    Image

    Image

    Basic properties

    vertex count | 70
edge count | 105
connected component count | 1

    Graph features

    asymmetric | bicolorable | biconnected | bicubic | bipartite | bridgeless | cage | class 1 | connected | cubic | cyclic | Hamilton-decomposable | Hamiltonian | Hamilton-laceable | H-star connected | LCF | local | noncayley | nonempty | noneulerian | nonplanar | perfect | perfect matching | regular | simple | square-free | traceable | triangle-free | weakly perfect | weakly regular

    Complement graph

    (not a named graph)

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 3 (70 vertices)

    Topological properties

    radius | 6
diameter | 6
girth | 10
vertex connectivity | 3
edge connectivity | 3

    Graph polynomials

    (x - 3) (x - 2) (x - 1)^8 x^2 (x + 1)^8 (x + 2) (x + 3) (x^2 - 6)^2 (x^2 - 5)^4 (x^2 - 2)^2 (x^4 - 6 x^2 + 3)^8

    Coloring properties

    chromatic number | 2
edge chromatic number | 3

    Spectrum

    (-3)^1 (-2.44949)^2 (-2.33441)^8 (-2.23607)^4 (-2)^1 (-1.41421)^2 (-1)^8 (-0.741964)^8 0^2 0.741964^8 1^8 1.41421^2 2^1 2.23607^4 2.33441^8 2.44949^2 3^1

    Associated matrices

    Associated matrices Adjacency matrix

    Associated matrices Incidence matrix

    Graph indices

    Hosoya index | 479 quadrillion
Kirchhoff index | 2726
stability index | 731.6 quadrillion
Wiener index | 9485

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