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    (1, 6, 3)-honeycomb Toroidal Graph

    Image

    Notation

    K_(3, 3)

    Basic properties

    vertex count | 6 edge count | 9 connected component count | 1

    Graph features

    apex | arc-transitive | bicolorable | biconnected | bicubic | bipartite | biplanar | bridgeless | cage | Cayley graphs | chromatically unique | circulant | class 1 | complete bipartite | complete k-partite | connected | critical nonplanar | cubic | cyclic | determined by resistance | determined by spectrum | distance-regular | distance-transitive | edge-transitive | Goethals-Seidel block design | graceful | Haar | Hamilton-decomposable | Hamiltonian | Hamilton-laceable | Harary | honeycomb toroidal | H-star connected | integral | Kuratowski | Laman | LCF | local | Möbius ladder | Moore | nonempty | noneulerian | nonplanar | Ore | perfect | perfect matching | projective planar | regular | simple | singlecross | strongly perfect | strongly regular | symmetric | toroidal | traceable | transposition | triangle-free | Turán | uniquely colorable | vertex-transitive | weakly perfect | well covered

    Complement graph

    two triangles

    Line graph

    generalized quadrangle (2, 1)

    Graph degrees

    vertex degrees | 3 (6 vertices)

    Topological properties

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

    Graph polynomials

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

    x^5 y^4 + 9 x^5 y^3 + 36 x^5 y^2 + 78 x^5 y + 81 x^5 + 6 x^4 y^2 + 45 x^4 y + 117 x^4 + 9 x^3 y + 84 x^3 + 36 x^2 + 9 x + 1

    x^5 + 4 x^4 + 10 x^3 + 9 x^2 y + 11 x^2 + 6 x y^2 + 15 x y + 5 x + y^4 + 5 y^3 + 9 y^2 + 5 y

    Coloring properties

    chromatic number | 2 edge chromatic number | 3

    Spectrum

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

    Associated matrices

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

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

    Graph indices

    Hosoya index | 34 Kirchhoff index | 9 stability index | 10 Wiener index | 21

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