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    4-dipyramidal Graph

    Image

    Image

    Notation

    K_(2, 2, 2)

    Alternate names

    (2, 2, 2)-complete 3-partite graph | (2, 2, 2)-complete tripartite graph | (3, 2)-wreath graph | 3-antiprism graph | 3-cocktail party graph | 3-triangular honeycomb queen graph | (4, 2)-Johnson graph | (4, 6)-Harary graph | 4-bipyramidal graph | 4-dipyramidal graph | ...

    Basic properties

    vertex count | 6 edge count | 12 connected component count | 1

    Graph features

    antiprism | apex | arc-transitive | biconnected | bridgeless | Cayley graphs | chromatically unique | circulant | class 1 | claw-free | cocktail party | complete k-partite | completely regular | complete tripartite | connected | cyclic | determined by resistance | determined by spectrum | dipyramid | distance-regular | distance-transitive | edge-transitive | Eulerian | Hamilton-connected | Hamilton-decomposable | Hamiltonian | Harary | H-star connected | integral | Johnson | LCF | line graphs | local | nonempty | Ore | pancyclic | perfect | perfect matching | planar | Platonic | polyhedral | quartic | regular | simple | strongly perfect | strongly regular | symmetric | traceable | triangular | triangular honeycomb queen | triangulated | Turán | vertex-transitive | weakly perfect | well covered | wreath

    Complement graph

    3-ladder rung graph

    Dual graph

    cubical graph

    Line graph

    octahedral line graph

    Graph degrees

    vertex degrees | 4 (6 vertices)

    Topological properties

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

    Graph polynomials

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

    x^5 y^7 + 12 x^5 y^6 + 66 x^5 y^5 + 220 x^5 y^4 + 489 x^5 y^3 + 744 x^5 y^2 + 740 x^5 y + 384 x^5 + 6 x^4 y^4 + 48 x^4 y^3 + 184 x^4 y^2 + 396 x^4 y + 408 x^4 + 12 x^3 y^2 + 87 x^3 y + 212 x^3 + 8 x^2 y + 66 x^2 + 12 x + 1

    x^5 + 7 x^4 + 8 x^3 y + 20 x^3 + 12 x^2 y^2 + 39 x^2 y + 25 x^2 + 6 x y^4 + 24 x y^3 + 52 x y^2 + 46 x y + 11 x + y^7 + 5 y^6 + 15 y^5 + 29 y^4 + 40 y^3 + 32 y^2 + 11 y

    Coloring properties

    chromatic number | 3 edge chromatic number | 4

    Spectrum

    (-2)^2 0^3 4^1

    Associated matrices

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

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

    Graph indices

    Hosoya index | 51 Kirchhoff index | 6.5 stability index | 13 Wiener index | 18

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