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    Gem Graph

    Image

    Image

    Alternate names

    (1, 4)-fan graph | 3-polyiamond 1 | 5-graph 29

    Basic properties

    vertex count | 5 edge count | 7 connected component count | 1

    Graph features

    apex | asymmetric | biconnected | bridgeless | chordal | chromatically nonunique | class 1 | claw-free | connected | cyclic | determined by resistance | determined by spectrum | fan | Hamiltonian | line graphs | matchstick | noncayley | nonempty | noneulerian | no perfect matching | pancyclic | perfect | planar | polyiamond | simple | traceable | unit-distance | weakly perfect

    Complement graph

    4-path and singleton

    Line graph

    7-graph 1009

    Graph degrees

    vertex degrees | 2 (2 vertices) | 3 (2 vertices) | 4 (1 vertex)

    Topological properties

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

    Graph polynomials

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

    x^4 y^3 + 7 x^4 y^2 + 19 x^4 y + 21 x^4 + 2 x^3 y^2 + 14 x^3 y + 32 x^3 + 3 x^2 y + 21 x^2 + 7 x + 1

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

    Coloring properties

    chromatic number | 3 edge chromatic number | 4

    Spectrum

    (1/2 (-1 - sqrt(5)))^1 (root of -2 - 5 x - x^2 + x^3 near x = -1.47283)^1 (root of -2 - 5 x - x^2 + x^3 near x = -0.462598)^1 (1/2 (-1 + sqrt(5)))^1 (root of -2 - 5 x - x^2 + x^3 near x = 2.93543)^1

    Associated matrices

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

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

    Graph indices

    Hosoya index | 15 Kirchhoff index | 6.952 stability index | 8 Wiener index | 13

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