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    6-graph 37

    Image

    Notation

    C_3 union P_2 union K_1

    Basic properties

    vertex count | 6 edge count | 4 connected component count | 3

    Graph features

    apex | asymmetric | block | bridged | chordal | chordless | chromatically nonunique | class 2 | claw-free | cyclic | determined by resistance | determined by spectrum | disconnected | dominating nonunique | flexible | integral | line graphs | linklessly embeddable | map | matchstick | Meyniel | multigraphic | noncayley | nonempty | noneulerian | nongeometric | nonhamiltonian | no perfect matching | outerplanar | perfect | planar | projective planar | pseudoforest | Ptolemaic | simple | square-free | strongly perfect | switchable | triangular honeycomb rook | ungraceful | unicyclic | uniquely embeddable | unit-distance | untraceable | weakly perfect | well covered

    Complement graph

    (1, 2, 3)-complete tripartite graph

    Line graph

    triangle and singleton

    Graph degrees

    vertex degrees | 0 (1 vertex) | 1 (2 vertices) | 2 (3 vertices)

    Topological properties

    radius | ∞ diameter | ∞ girth | 3 vertex connectivity | 0 edge connectivity | 0

    Graph polynomials

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

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

    x (x^2 + x + y)

    Coloring properties

    chromatic number | 3 edge chromatic number | 3

    Spectrum

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

    Associated matrices

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

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

    Graph indices

    Hosoya index | 8 Kirchhoff index | ∞ stability index | 8 Wiener index | ∞