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    12-circulant Graph (2)

    Image

    Notation

    2C_6

    Basic properties

    vertex count | 12 edge count | 12 connected component count | 2

    Graph features

    apex | arc-transitive | bicolorable | bipartite | bridgeless | Cayley graphs | chordless | circulant | class 1 | claw-free | cyclic | disconnected | distance-regular | distance-transitive | edge-transitive | flexible | graceful | Haar | integral | line graphs | linklessly embeddable | local | map | matchstick | Meyniel | multigraphic | nonempty | noneulerian | nongeometric | nonhamiltonian | not determined by resistance | not determined by spectrum | outerplanar | perfect | perfect matching | planar | projective planar | pseudoforest | regular | simple | square-free | switchable | symmetric | Taylor | triangle-free | two-regular | uniquely embeddable | unit-distance | untraceable | vertex-transitive | weakly perfect | weakly regular

    Complement graph

    12-circulant graph (1, 3, 4, 5, 6)

    Line graph

    two hexagons

    Graph degrees

    vertex degrees | 2 (12 vertices)

    Topological properties

    radius | ∞ diameter | ∞ girth | 6 vertex connectivity | 0 edge connectivity | 0

    Graph polynomials

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

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

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

    Coloring properties

    chromatic number | 2 edge chromatic number | 2

    Spectrum

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

    Associated matrices

    Graph indices

    Hosoya index | 324 Kirchhoff index | ∞ stability index | 400 Wiener index | ∞