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    (3, 1)-lollipop Graph

    Image

    Basic properties

    vertex count | 4 edge count | 4 connected component count | 1

    Graph features

    almost Hamiltonian | apex | asymmetric | bridged | cactus | chordal | chordless | chromatically unique | class 1 | claw-free | connected | cyclic | determined by resistance | determined by spectrum | geodetic | graceful | line graphs | lollipop | matchstick | maximally nonhamiltonian | noncayley | nonempty | noneulerian | nonhamiltonian | outerplanar | pan | perfect | perfect matching | planar | projective planar | pseudoforest | pseudotree | simple | split | square-free | strongly perfect | tadpole | traceable | unicyclic | unit-distance | weakly perfect

    Complement graph

    3-path and singleton

    Line graph

    diamond graph

    Graph degrees

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

    Topological properties

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

    Graph polynomials

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

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

    x (x^2 + x + y)

    Coloring properties

    chromatic number | 3 edge chromatic number | 3

    Spectrum

    (root of 1 - 3 x - x^2 + x^3 near x = -1.48119)^1 (-1)^1 (root of 1 - 3 x - x^2 + x^3 near x = 0.311108)^1 (root of 1 - 3 x - x^2 + x^3 near x = 2.17009)^1

    Associated matrices

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

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

    Graph indices

    Hosoya index | 6 Kirchhoff index | 6.333 stability index | 6 Wiener index | 8

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