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    14-vertex Transitive Graph 20

    Image

    Notation

    (K_2 square K_7)^_

    Basic properties

    vertex count | 14 edge count | 42 connected component count | 1

    Graph features

    antipodal | arc-transitive | bicolorable | biconnected | bipartite | bipartite Kneser | bridgeless | Cayley graphs | circulant | class 1 | conformally rigid | connected | crown | cyclic | distance-regular | distance-transitive | edge-transitive | Eulerian | fully reconstructible in C^1 | geometric | Haar | Hamilton-decomposable | Hamiltonian | Hamilton-laceable | H-star connected | integral | intrinsically linked | LCF | local | Meyniel | multigraphic | nonempty | nonplanar | not uniquely embeddable | perfect | perfect matching | regular | rigid | rook complement | sextic | simple | switchable | symmetric | Taylor | traceable | triangle-free | ungraceful | uniquely colorable | vertex-transitive | weakly perfect | weakly regular

    Complement graph

    (2, 7)-rook graph

    Line graph

    (not a named graph)

    Graph degrees

    vertex degrees | 6 (14 vertices)

    Topological properties

    radius | 3 diameter | 3 girth | 4 vertex connectivity | 6 edge connectivity | 6

    Graph polynomials

    (x - 6) (x - 1)^6 (x + 1)^6 (x + 6)

    x^13 y^29 + 42 x^13 y^28 + 861 x^13 y^27 + 11480 x^13 y^26 + 111930 x^13 y^25 + 850668 x^13 y^24 + 14 x^12 y^24 + 5245772 x^13 y^23 + 504 x^12 y^23 + ... + 25155948 x^7 + 5096441 x^6 + 842688 x^5 + 111720 x^4 + 11480 x^3 + 861 x^2 + 42 x + 1 (147 terms)

    y^29 + 13 y^28 + 91 y^27 + 455 y^26 + 1820 y^25 + 14 x y^24 + 6174 y^24 + 168 x y^23 + 18382 y^23 + 1092 x y^22 + ... + 4285 x^10 + 30290 x^9 + 159531 x^8 + 634166 x^7 + 1896095 x^6 + 4187370 x^5 + 6589742 x^4 + 6932252 x^3 + 4316107 x^2 + 1181276 x (146 terms)

    Coloring properties

    chromatic number | 2 edge chromatic number | 6

    Spectrum

    (-6)^1 (-1)^6 1^6 6^1

    Associated matrices

    Graph indices

    Hosoya index | 63840 Kirchhoff index | 29.97 stability index | 2368 Wiener index | 147