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    Hajós Graph

    Image

    Image

    Alternate names

    7-graph 928 | Hajós graph

    Basic properties

    vertex count | 7 edge count | 11 connected component count | 1

    Graph features

    apex | asymmetric | biconnected | bridgeless | chromatically nonunique | class 1 | claw-free | connected | cyclic | determined by resistance | determined by spectrum | Hamiltonian | imperfect | noncayley | nonempty | noneulerian | no perfect matching | pancyclic | planar | simple | traceable | unit-distance | well covered

    Complement graph

    7-graph 733

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 3 (6 vertices) | 4 (1 vertex)

    Topological properties

    radius | 2 diameter | 2 girth | 3 vertex connectivity | 2 edge connectivity | 3

    Graph polynomials

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

    x^6 y^5 + 11 x^6 y^4 + 55 x^6 y^3 + 157 x^6 y^2 + 256 x^6 y + 192 x^6 + 8 x^5 y^3 + 74 x^5 y^2 + 254 x^5 y + 336 x^5 + 16 x^4 y^2 + 124 x^4 y + 296 x^4 + 2 x^3 y^2 + 34 x^3 y + 161 x^3 + 4 x^2 y + 55 x^2 + 11 x + 1

    x^6 + 5 x^5 + 4 x^4 y + 11 x^4 + 2 x^3 y^2 + 14 x^3 y + 15 x^3 + 10 x^2 y^2 + 26 x^2 y + 12 x^2 + 8 x y^3 + 24 x y^2 + 20 x y + 4 x + y^5 + 6 y^4 + 13 y^3 + 12 y^2 + 4 y

    Coloring properties

    chromatic number | 4 edge chromatic number | 4

    Spectrum

    (root of 4 - 5 x - 2 x^2 + x^3 near x = -1.85577)^1 (-sqrt(3))^1 (-1)^2 (root of 4 - 5 x - 2 x^2 + x^3 near x = 0.678363)^1 sqrt(3)^1 (root of 4 - 5 x - 2 x^2 + x^3 near x = 3.17741)^1

    Associated matrices

    (0 | 1 | 0 | 0 | 1 | 0 | 1 1 | 0 | 1 | 0 | 0 | 1 | 0 0 | 1 | 0 | 1 | 0 | 1 | 0 0 | 0 | 1 | 0 | 1 | 1 | 1 1 | 0 | 0 | 1 | 0 | 0 | 1 0 | 1 | 1 | 1 | 0 | 0 | 0 1 | 0 | 0 | 1 | 1 | 0 | 0)

    (1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1)

    Graph indices

    Hosoya index | 60 Kirchhoff index | 14.5 stability index | 48 Wiener index | 31

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