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    Star Graph

    Image

    Image

    Alternate name

    Hochberg-O'Donnell graph 45

    Basic properties

    vertex count | 45 edge count | 85 connected component count | 1

    Graph features

    asymmetric | biconnected | bridgeless | class 1 | connected | cyclic | Hamilton-connected | Hamiltonian | H-star connected | imperfect | noncayley | nonempty | noneulerian | nonplanar | no perfect matching | simple | square-free | traceable | triangle-free | unit-distance

    Complement graph

    (not a named graph)

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 3 (35 vertices) | 6 (5 vertices) | 7 (5 vertices)

    Topological properties

    radius | 3 diameter | 4 girth | 5 vertex connectivity | 3 edge connectivity | 3

    Graph polynomials

    -(x^3 + x^2 - 2 x - 1) (x^6 - 5 x^5 - 4 x^4 + 35 x^3 - 26 x^2 - 10 x + 8) (x^18 + 2 x^17 - 31 x^16 - 52 x^15 + 400 x^14 + ... + 9232 x^2 - 119 x - 1 (19 terms))^2

    Coloring properties

    chromatic number | 4 edge chromatic number | 7

    Spectrum

    (-3.32026)^2 (-3.16465)^2 (-2.64639)^1 (-2.23882)^2 (-1.89138)^2 (-1.80194)^1 (-1.75836)^2 (-1.64422)^2 (-1.10058)^2 (-1.0893)^2 (-0.544502)^1 (-0.445042)^1 (-0.005793)^2 0.0188314^2 0.538712^1 1.00424^2 1.10107^1 1.16886^2 1.24698^1 1.26108^2 1.30168^2 2.10531^1 2.14267^2 2.22022^2 2.46332^2 2.63248^2 4.44581^1

    Associated matrices

    Associated matrices Adjacency matrix

    Associated matrices Incidence matrix

    Graph indices

    Hosoya index | 1.626 trillion Kirchhoff index | 813.7 stability index | 2.418 trillion Wiener index | 2670

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