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    (3, 1)-Cayley Tree

    Image

    Notation

    K_(1, 3)

    Basic properties

    vertex count | 4 edge count | 3 connected component count | 1

    Graph features

    acyclic | apex | asymmetric | Beineke | bicolorable | bipartite | block | bridged | cactus | caterpillar | chordal | chordless | chromatically nonunique | class 1 | complete bipartite | complete k-partite | complete tree | conformally rigid | connected | determined by resistance | determined by spectrum | distance-hereditary | dominating unique | edge-transitive | flexible | forest | geodetic | graceful | k-tree | linklessly embeddable | lobster | Lucas cube | map | matchstick | median | Metelsky | Meyniel | noncayley | nonempty | noneulerian | nongeometric | nonhamiltonian | no perfect matching | outerplanar | perfect | planar | projective planar | pseudoforest | pseudotree | Ptolemaic | quadratically embeddable | series-reduced | simple | spider | split | spoke | square-free | stacked book | star | strongly perfect | tree | triangle-free | tripod | unigraphic | uniquely colorable | uniquely embeddable | uniquely graceful | unit-distance | unswitchable | untraceable | weakly perfect

    Complement graph

    triangle and singleton

    Line graph

    triangle graph

    Graph degrees

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

    Topological properties

    radius | 1 diameter | 2 girth | ∞ vertex connectivity | 1 edge connectivity | 1

    Graph polynomials

    x^2 (x^2 - 3)

    (x + 1)^3

    x^3

    Coloring properties

    chromatic number | 2 edge chromatic number | 3

    Spectrum

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

    Associated matrices

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

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

    Graph indices

    Hosoya index | 4 Kirchhoff index | 9 stability index | 4 Wiener index | 9