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    Shrikhande Graph

    Image

    Basic properties

    vertex count | 16 edge count | 48 connected component count | 1

    Graph features

    arc-transitive | biconnected | bridgeless | Cayley graphs | class 1 | conformally rigid | connected | cyclic | distance-regular | Doob | edge-transitive | Eulerian | fully reconstructible in C^1 | graceful | Hamilton-connected | Hamilton-decomposable | Hamiltonian | H-star connected | imperfect | integral | LCF | local | multigraphic | nonempty | nongeometric | nonplanar | not determined by resistance | not determined by spectrum | not uniquely embeddable | pancyclic | perfect matching | quadratically embeddable | regular | rigid | sextic | simple | strongly regular | switchable | symmetric | toroidal | torus triangulation | traceable | vertex-transitive | zero-two

    Complement graph

    Shrikhande complement graph

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 6 (16 vertices)

    Topological properties

    radius | 2 diameter | 2 girth | 3 vertex connectivity | 6 edge connectivity | 6

    Graph polynomials

    (x - 6) (x - 2)^6 (x + 2)^9

    x^15 y^33 + 48 x^15 y^32 + 1128 x^15 y^31 + 17296 x^15 y^30 + 194580 x^15 y^29 + 1712304 x^15 y^28 + 16 x^14 y^28 + 12271496 x^15 y^27 + ... + 67886976 x^7 + 11752192 x^6 + 1677792 x^5 + 193080 x^4 + 17264 x^3 + 1128 x^2 + 48 x + 1 (202 terms)

    y^33 + 15 y^32 + 120 y^31 + 680 y^30 + 3060 y^29 + 16 x y^28 + 11612 y^28 + 224 x y^27 + 38520 y^27 + ... + 1046271 x^9 + 3714211 x^8 + 10441875 x^7 + 22965799 x^6 + 38581071 x^5 + 47577407 x^4 + 40316242 x^3 + 20782058 x^2 + 4851764 x (201 terms)

    Coloring properties

    chromatic number | 4 edge chromatic number | 6

    Spectrum

    (-2)^9 2^6 6^1

    Associated matrices

    Graph indices

    Hosoya index | 269921 Kirchhoff index | 42 stability index | 492593 Wiener index | 192