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    (3, 3)-rook Graph

    Image

    Image

    Notation

    GQ(2, 1)

    Alternate names

    (2, 3)-Hamming graph | 2-Bartolo-Borg-Scicluna graph | (3, 3)-KC graph | (3, 3)-lattice graph | (3, 3)-rook complement graph | (3, 3)-rook graph | (3, 3)-torus grid graph | 9-arc transitive graph 2 | 9-edge-transitive graph 9 | 9-graph 262066 | ...

    Basic properties

    vertex count | 9 edge count | 18 connected component count | 1

    Graph features

    apex | arc-transitive | biconnected | biplanar | bridgeless | Cayley graphs | chromatically nonunique | class 2 | claw-free | conference | conformally rigid | connected | critical nonplanar | cyclic | determined by resistance | determined by spectrum | distance-regular | distance-transitive | dominating nonunique | edge-transitive | Eulerian | fully reconstructible in C^1 | generalized polygon | geometric | Hamilton-connected | Hamilton-decomposable | Hamiltonian | Hamming | H-star connected | integral | KC | LCF | line graphs | linklessly embeddable | local | multigraphic | nonempty | nonplanar | no perfect matching | not uniquely embeddable | Paley | pancyclic | Peisert | perfect | projective planar | quadratically embeddable | quartic | regular | rigid | rook | rook complement | self-complementary | simple | strongly regular | switchable | symmetric | toroidal | torus grid | traceable | ungraceful | unit-distance | vertex-transitive | weakly perfect | well covered

    Complement graph

    generalized quadrangle (2, 1)

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 4 (9 vertices)

    Topological properties

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

    Graph polynomials

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

    x^8 y^10 + 18 x^8 y^9 + 153 x^8 y^8 + 816 x^8 y^7 + 3051 x^8 y^6 + 8442 x^8 y^5 + 17721 x^8 y^4 + 28296 x^8 y^3 + 33534 x^8 y^2 + 27216 x^8 y + 11664 x^8 + ... + 3939 x^5 y + 7776 x^5 + 51 x^4 y^2 + 792 x^4 y + 2961 x^4 + 99 x^3 y + 810 x^3 + 6 x^2 y + 153 x^2 + 18 x + 1 (39 terms)

    x^8 + 10 x^7 + 6 x^6 y + 49 x^6 + 63 x^5 y + 151 x^5 + 51 x^4 y^2 + 285 x^4 y + 310 x^4 + 6 x^3 y^4 + 66 x^3 y^3 + 354 x^3 y^2 + 711 x^3 y + 409 x^3 + ... + 1101 x y^2 + 582 x y + 98 x + y^10 + 8 y^9 + 36 y^8 + 111 y^7 + 258 y^6 + 462 y^5 + 636 y^4 + 623 y^3 + 372 y^2 + 98 y (38 terms)

    Coloring properties

    chromatic number | 3 edge chromatic number | 5

    Spectrum

    (-2)^4 1^4 4^1

    Associated matrices

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

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

    Graph indices

    Hosoya index | 370 Kirchhoff index | 18 stability index | 112 Wiener index | 54

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