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    8-circulant Graph (4)

    Image

    Notation

    4P_2

    Basic properties

    vertex count | 8 edge count | 4 connected component count | 4

    Graph features

    acyclic | apex | arc-transitive | bicolorable | bipartite | bridged | Cayley graphs | chordal | chordless | chromatically nonunique | circulant | class 1 | claw-free | determined by resistance | determined by spectrum | disconnected | distance-regular | distance-transitive | edge-transitive | forest | Haar | integral | Knödel | ladder rung | line graphs | matchstick | nonempty | noneulerian | nonhamiltonian | outerplanar | perfect | perfect matching | planar | projective planar | pseudoforest | regular | simple | square-free | strongly perfect | strongly regular | symmetric | triangle-free | ungraceful | uniquely colorable | unit-distance | untraceable | vertex-transitive | weakly perfect | well covered

    Complement graph

    16-cell graph

    Line graph

    4-empty graph

    Graph degrees

    vertex degrees | 1 (8 vertices)

    Topological properties

    radius | ∞ diameter | ∞ girth | ∞ vertex connectivity | 0 edge connectivity | 0

    Graph polynomials

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

    (x + 1)^4

    x^4

    Coloring properties

    chromatic number | 2 edge chromatic number | 1

    Spectrum

    (-1)^4 1^4

    Associated matrices

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

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

    Graph indices

    Hosoya index | 16 Kirchhoff index | ∞ stability index | 16 Wiener index | ∞

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