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    7-graph 392

    Image

    Notation

    TS_7

    Basic properties

    vertex count | 7 edge count | 9 connected component count | 1

    Graph features

    apex | asymmetric | bridgeless | cactus | chordal | chordless | chromatically nonunique | class 1 | claw-free | connected | cyclic | determined by resistance | determined by spectrum | Eulerian | geodetic | line graphs | matchstick | noncayley | nonempty | nonhamiltonian | no perfect matching | outerplanar | perfect | planar | projective planar | simple | square-free | traceable | triangular snake | ungraceful | unit-distance | weakly perfect

    Complement graph

    7-graph 885

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 2 (5 vertices) | 4 (2 vertices)

    Topological properties

    radius | 2 diameter | 3 girth | 3 vertex connectivity | 1 edge connectivity | 2

    Graph polynomials

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

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

    (x^2 + x + y)^3

    Coloring properties

    chromatic number | 3 edge chromatic number | 4

    Spectrum

    (-sqrt(3))^1 (root of 2 - 3 x - 2 x^2 + x^3 near x = -1.34292)^1 (-1)^2 (root of 2 - 3 x - 2 x^2 + x^3 near x = 0.529317)^1 sqrt(3)^1 (root of 2 - 3 x - 2 x^2 + x^3 near x = 2.81361)^1

    Associated matrices

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

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

    Graph indices

    Hosoya index | 36 Kirchhoff index | 24.67 stability index | 32 Wiener index | 37

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