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    (3, 1, 1)-I Graph

    Image

    Image

    Notation

    P_2 square C_3

    Alternate names

    1-Plummer-Toft graph | (2, 3)-KC graph | (2, 3)-lattice graph | (2, 3)-rook graph | (3, 1, 1)-I graph | (3, 1)-generalized Petersen graph | (3, 2)-generalized prism graph | (3, 2)-KP graph | (3, 2)-stacked prism graph | 3-circular ladder graph | ...

    Basic properties

    vertex count | 6 edge count | 9 connected component count | 1

    Graph features

    apex | asymmetric | biconnected | bridgeless | Cayley graphs | chromatically unique | circulant | class 1 | claw-free | connected | cubic | cycle complement | cyclic | determined by resistance | determined by spectrum | dominating nonunique | fully reconstructible in C^1 | generalized Petersen | graceful | Halin | Hamilton-connected | Hamilton-decomposable | Hamiltonian | H-star connected | I graphs | integral | KC | KP | Laman | LCF | line graphs | linklessly embeddable | local | map | multigraphic | nonempty | noneulerian | nongeometric | Ore | pancyclic | perfect | perfect matching | planar | Plummer-Toft | polyhedral | prism | projective planar | quadratically embeddable | regular | rigid | rook | simple | stacked prism | switchable | traceable | uniquely embeddable | unit-distance | vertex-transitive | weakly perfect | weakly regular | well covered

    Complement graph

    6-cycle graph

    Dual graph

    3-dipyramidal graph

    Line graph

    9-quartic graph 5

    Graph degrees

    vertex degrees | 3 (6 vertices)

    Topological properties

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

    Graph polynomials

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

    x^5 y^4 + 9 x^5 y^3 + 36 x^5 y^2 + 77 x^5 y + 75 x^5 + 7 x^4 y^2 + 51 x^4 y + 111 x^4 + 15 x^3 y + 82 x^3 + 2 x^2 y + 36 x^2 + 9 x + 1

    x^5 + 4 x^4 + 2 x^3 y + 8 x^3 + 9 x^2 y + 9 x^2 + 7 x y^2 + 13 x y + 4 x + y^4 + 5 y^3 + 8 y^2 + 4 y

    Coloring properties

    chromatic number | 3 edge chromatic number | 3

    Spectrum

    (-2)^2 0^2 1^1 3^1

    Associated matrices

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

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

    Graph indices

    Hosoya index | 32 Kirchhoff index | 9.4 stability index | 22 Wiener index | 21

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