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    Butterfly Graph

    Image

    Image

    Alternate names

    (2, 3)-Dutch windmill graph | (2, 3)-windmill graph | 2-friendship graph | (3, 3)-black bishop graph | 5-graph 23 | bowtie graph

    Basic properties

    vertex count | 5 edge count | 6 connected component count | 1

    Graph features

    almost Hamiltonian | apex | asymmetric | black bishop | bridgeless | cactus | chordal | chordless | chromatically nonunique | class 1 | claw-free | connected | cyclic | determined by resistance | determined by spectrum | Dutch windmill | Eulerian | line graphs | matchstick | maximally nonhamiltonian | noncayley | nonempty | nonhamiltonian | no perfect matching | perfect | planar | simple | square-free | strongly perfect | traceable | unit-distance | weakly perfect

    Complement graph

    square and singleton

    Line graph

    6-graph 135

    Graph degrees

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

    Topological properties

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

    Graph polynomials

    -(x - 1) (x + 1)^2 (x^2 - x - 4)

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

    (x^2 + x + y)^2

    Coloring properties

    chromatic number | 3 edge chromatic number | 4

    Spectrum

    (1/2 (1 - sqrt(17)))^1 (-1)^2 1^1 (1/2 (1 + sqrt(17)))^1

    Associated matrices

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

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

    Graph indices

    Hosoya index | 12 Kirchhoff index | 9.333 stability index | 8 Wiener index | 14

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