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    (1, 12, 1)-honeycomb Toroidal Graph

    Image

    Notation

    C_12

    Basic properties

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

    Graph features

    antipodal | apex | arc-transitive | bicolorable | biconnected | bipartite | bridgeless | cactus | Cayley graphs | chordless | chromatically unique | circulant | class 1 | claw-free | connected | cycle | cyclic | determined by spectrum | distance-regular | distance-transitive | edge-transitive | Eulerian | graceful | Haar | Hamilton-decomposable | Hamiltonian | Harary | honeycomb toroidal | Knödel | LCF | line graphs | local | matchstick | nonempty | outerplanar | perfect | perfect matching | planar | projective planar | pseudoforest | pseudotree | regular | simple | square-free | symmetric | traceable | triangle-free | two-regular | unicyclic | uniquely colorable | unit-distance | vertex-transitive | weakly perfect | weakly regular | wreath

    Complement graph

    12-circulant graph (1, 2, 3, 4, 6)

    Line graph

    12-cycle graph

    Graph degrees

    vertex degrees | 2 (12 vertices)

    Topological properties

    radius | 6 diameter | 6 girth | 12 vertex connectivity | 2 edge connectivity | 2

    Graph polynomials

    (x - 2) (x - 1)^2 x^2 (x + 1)^2 (x + 2) (x^2 - 3)^2

    x^11 y + 12 x^11 + 66 x^10 + 220 x^9 + 495 x^8 + 792 x^7 + 924 x^6 + 792 x^5 + 495 x^4 + 220 x^3 + 66 x^2 + 12 x + 1

    x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + y

    Coloring properties

    chromatic number | 2 edge chromatic number | 2

    Spectrum

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

    Associated matrices

    Graph indices

    Hosoya index | 322 Kirchhoff index | 143 stability index | 320 Wiener index | 216

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