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    (1, 6, 1)-honeycomb Toroidal Graph

    Image

    Notation

    C_6

    Basic properties

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

    Graph features

    antipodal | apex | arc-transitive | arrangement | bicolorable | biconnected | bipartite | bipartite Kneser | Bouwer | bridgeless | Bruhat | cactus | Cayley graphs | chordless | chromatically unique | circulant | class 1 | claw-free | connected | crown | cycle | cyclic | determined by resistance | determined by spectrum | distance-regular | distance-transitive | edge-transitive | Eulerian | fusene | Haar | Hamilton-decomposable | Hamiltonian | Harary | hexagonal grid | honeycomb toroidal | integral | Knödel | LCF | line graphs | local | matchstick | nonempty | outerplanar | perfect | perfect matching | permutation star | planar | polyhex | projective planar | pseudoforest | pseudotree | regular | rook complement | simple | square-free | stacked prism | symmetric | Taylor | traceable | triangle-free | two-regular | ungraceful | unicyclic | uniquely colorable | unit-distance | vertex-transitive | weakly perfect | weakly regular | wreath

    Complement graph

    3-prism graph

    Line graph

    6-cycle graph

    Graph degrees

    vertex degrees | 2 (6 vertices)

    Topological properties

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

    Graph polynomials

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

    x^5 y + 6 x^5 + 15 x^4 + 20 x^3 + 15 x^2 + 6 x + 1

    x^5 + x^4 + x^3 + x^2 + x + y

    Coloring properties

    chromatic number | 2 edge chromatic number | 2

    Spectrum

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

    Associated matrices

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

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

    Graph indices

    Hosoya index | 18 Kirchhoff index | 17.5 stability index | 20 Wiener index | 27

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