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    8-graph 12047

    Image

    Notation

    K_8-2K_(2, 3)

    Alternate name
    Basic properties

    vertex count | 8 edge count | 22 connected component count | 1

    Graph features

    asymmetric | biconnected | biplanar | bridgeless | chordal | chordless | chromatically nonunique | class 1 | claw-free | connected | cyclic | determined by resistance | determined by spectrum | double-toroidal | Hamilton-connected | Hamiltonian | H-star connected | noncayley | nonempty | noneulerian | nonplanar | Ore | pancyclic | perfect | perfect matching | simple | strongly perfect | traceable | ungraceful | weakly perfect

    Complement graph

    (not a named graph)

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 4 (2 vertices) | 5 (3 vertices) | 7 (3 vertices)

    Topological properties

    radius | 1 diameter | 2 girth | 3 vertex connectivity | 3 edge connectivity | 4

    Graph polynomials

    (x + 1)^5 (x^3 - 5 x^2 - 7 x + 17)

    x^7 y^15 + 22 x^7 y^14 + 231 x^7 y^13 + 1540 x^7 y^12 + 7313 x^7 y^11 + 26295 x^7 y^10 + 74255 x^7 y^9 + 168487 x^7 y^8 + 311472 x^7 y^7 + 472439 x^7 y^6 + ... + 6123 x^4 y + 6686 x^4 + 20 x^3 y^3 + 138 x^3 y^2 + 629 x^3 y + 1511 x^3 + 29 x^2 y + 231 x^2 + 22 x + 1 (55 terms)

    x^7 + 15 x^6 + 29 x^5 y + 91 x^5 + 20 x^4 y^3 + 78 x^4 y^2 + 268 x^4 y + 285 x^4 + 7 x^3 y^6 + 34 x^3 y^5 + 121 x^3 y^4 + 318 x^3 y^3 + ... + 82 y^12 + 193 y^11 + 385 y^10 + 670 y^9 + 1036 y^8 + 1434 y^7 + 1775 y^6 + 1934 y^5 + 1785 y^4 + 1290 y^3 + 624 y^2 + 144 y (54 terms)

    Coloring properties

    chromatic number | 6 edge chromatic number | 7

    Spectrum

    (root of 17 - 7 x - 5 x^2 + x^3 near x = -2.1142)^1 (-1)^5 (root of 17 - 7 x - 5 x^2 + x^3 near x = 1.40952)^1 (root of 17 - 7 x - 5 x^2 + x^3 near x = 5.70468)^1

    Associated matrices

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

    Graph indices

    Hosoya index | 368 Kirchhoff index | 9.933 stability index | 200 Wiener index | 34

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