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    7-wheel Complement Graph

    Image

    Notation

    Y_3 union K_1

    Basic properties

    vertex count | 7 edge count | 9 connected component count | 2

    Graph features

    apex | asymmetric | bridgeless | chromatically unique | class 1 | claw-free | cyclic | determined by resistance | determined by spectrum | disconnected | dominating nonunique | flexible | graceful | integral | line graphs | linklessly embeddable | map | multigraphic | noncayley | nonempty | noneulerian | nongeometric | nonhamiltonian | no perfect matching | perfect | planar | projective planar | simple | switchable | uniquely embeddable | unit-distance | untraceable | weakly perfect | well covered | wheel complement

    Complement graph

    7-wheel graph

    Line graph

    9-quartic graph 5

    Graph degrees

    vertex degrees | 0 (1 vertex) | 3 (6 vertices)

    Topological properties

    radius | ∞ diameter | ∞ girth | 3 vertex connectivity | 0 edge connectivity | 0

    Graph polynomials

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

    x^5 y^4 + 9 x^5 y^3 + 36 x^5 y^2 + 77 x^5 y + 75 x^5 + 7 x^4 y^2 + 51 x^4 y + 111 x^4 + 15 x^3 y + 82 x^3 + 2 x^2 y + 36 x^2 + 9 x + 1

    x^5 + 4 x^4 + 2 x^3 y + 8 x^3 + 9 x^2 y + 9 x^2 + 7 x y^2 + 13 x y + 4 x + y^4 + 5 y^3 + 8 y^2 + 4 y

    Coloring properties

    chromatic number | 3 edge chromatic number | 3

    Spectrum

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

    Associated matrices

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

    Graph indices

    Hosoya index | 32 Kirchhoff index | ∞ stability index | 4 Wiener index | ∞