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    7-graph 1026

    Image

    Notation

    P^__7

    Alternate name
    Basic properties

    vertex count | 7 edge count | 15 connected component count | 1

    Graph features

    apex | asymmetric | biconnected | biplanar | bridgeless | chromatically nonunique | class 1 | claw-free | connected | cyclic | determined by resistance | determined by spectrum | dominating nonunique | fully reconstructible in C^1 | graceful | Hamilton-connected | Hamiltonian | H-star connected | linklessly embeddable | multigraphic | noncayley | nonempty | noneulerian | nongeometric | nonplanar | no perfect matching | not uniquely embeddable | Ore | pancyclic | path complement | perfect | projective planar | rigid | simple | singlecross | switchable | toroidal | traceable | weakly perfect | well covered

    Complement graph

    7-path graph

    Line graph

    (not a named graph)

    Graph degrees

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

    Topological properties

    radius | 2 diameter | 2 girth | 3 vertex connectivity | 4 edge connectivity | 4

    Graph polynomials

    (x + 1) (x^2 + 2 x - 1) (x^4 - 3 x^3 - 7 x^2 + 5 x + 2)

    x^6 y^9 + 15 x^6 y^8 + 105 x^6 y^7 + 455 x^6 y^6 + 1360 x^6 y^5 + 2946 x^6 y^4 + 4703 x^6 y^3 + 5455 x^6 y^2 + 4293 x^6 y + 1807 x^6 + 5 x^5 y^6 + ... + 309 x^4 y^2 + 876 x^4 y + 1224 x^4 + x^3 y^3 + 18 x^3 y^2 + 141 x^3 y + 445 x^3 + 10 x^2 y + 105 x^2 + 15 x + 1 (30 terms)

    x^6 + 9 x^5 + 10 x^4 y + 35 x^4 + x^3 y^3 + 15 x^3 y^2 + 68 x^3 y + 71 x^3 + 6 x^2 y^4 + 36 x^2 y^3 + 111 x^2 y^2 + 159 x^2 y + 72 x^2 + 5 x y^6 + 27 x ... (3 terms) + 80 x y^4 + 161 x y^3 + 207 x y^2 + 137 x y + 28 x + y^9 + 6 y^8 + 21 y^7 + 51 y^6 + 94 y^5 + 134 y^4 + 140 y^3 + 93 y^2 + 28 y

    Coloring properties

    chromatic number | 4 edge chromatic number | 5

    Spectrum

    (-1 - sqrt(2))^1 (root of 2 + 5 x - 7 x^2 - 3 x^3 + x^4 near x = -1.86933)^1 (-1)^1 (root of 2 + 5 x - 7 x^2 - 3 x^3 + x^4 near x = -0.29505)^1 (-1 + sqrt(2))^1 (root of 2 + 5 x - 7 x^2 - 3 x^3 + x^4 near x = 0.838187)^1 (root of 2 + 5 x - 7 x^2 - 3 x^3 + x^4 near x = 4.3262)^1

    Associated matrices

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

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

    Graph indices

    Hosoya index | 112 Kirchhoff index | 9.026 stability index | 40 Wiener index | 27