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    Harary Graph

    Graphs with available data

    triangle graph | square graph | tetrahedral graph | pentatope graph | 5-cycle graph | 5-wheel graph | octahedral graph | utility graph | 6-complete graph | 6-cycle graph | 7-circulant graph (1, 2) | 7-complete graph | 7-cycle graph | (3, 7)-Harary graph | (7, 4)-Turán graph | 16-cell graph | Wagner graph | 4-antiprism graph | 8-circulant graph (1, 2, 4) | 8-complete graph | ... (total: 128)

    Images

    Images

    Alternate names

    (1, 1, 1)-complete tripartite graph | (1, 2)-fan graph | (1, 3)-Hamming graph | (1, 3)-lattice graph | (1, 3)-queen graph | (1, 3)-rook graph | 1-Hanoi graph | 1-polyiamond 1 | 1-Sierpiński graph | 1-Sierpiński sieve graph | ...

    (1, 2, 2)-grid graph | (1, 2)-stacked book graph | (1, 4, 1)-honeycomb toroidal graph | 1-book graph | 1-polyomino graph 1 | (2, 1)-bipartite (0, 2)-graph | (2, 2)-complete 2-partite graph | (2, 2)-complete bipartite graph | (2, 2)-grid graph | (2, 2)-Hamming graph | ...

    0-crossing number graph A | (1, 4)-Hamming graph | (1, 4)-lattice graph | (1, 4)-queen graph | (1, 4)-rook graph | 1-Sierpiński tetrahedron graph | (2, 2)-king graph | (2, 2)-queen graph | 2-Apollonian graph | (3, 1)-nonbipartite (0, 2)-graph | ...

    (1, 5)-Hamming graph | (1, 5)-lattice graph | (1, 5)-queen graph | (1, 5)-rook graph | (4, 5)-Harary graph | (5, 1)-arrangement graph | (5, 1)-Johnson graph | (5, 1)-Kneser graph | (5, 5)-Turán graph | 5-circulant graph (1, 2) | ...

    (2, 5)-Harary graph | 2-Andrásfai graph | 3-Mycielski graph | (5, 1)-stacked prism graph | (5, 1)-wreath graph | 5-circulant graph (1) | 5-circulant graph (2) | 5-edge-transitive graph 9 | 5-graph 27 | 5-Paley graph | ...

    (1, 2, 2)-complete 3-partite graph | (1, 2, 2)-complete tripartite graph | (2, 3)-fan graph | (3, 5)-Harary graph | 4-diagonal intersection graph | (5, 3)-Turán graph | 5-graph 32 | Johnson solid skeleton 1 | pentahedral graph 1

    (2, 2, 2)-complete 3-partite graph | (2, 2, 2)-complete tripartite graph | (3, 2)-wreath graph | 3-antiprism graph | 3-cocktail party graph | 3-triangular honeycomb queen graph | (4, 2)-Johnson graph | (4, 6)-Harary graph | 4-bipyramidal graph | 4-dipyramidal graph | ...

    (1, 6, 3)-honeycomb toroidal graph | 1-crossing number graph A | (3, 3)-complete 2-partite graph | (3, 3)-complete bipartite graph | (3, 6)-Harary graph | 3-Möbius ladder graph | 3-Möbius wheel | 3-transposition graph | (6, 2)-Turán graph | 6-circulant graph (1, 3) | ...

    (1, 6)-Hamming graph | (1, 6)-lattice graph | (1, 6)-queen graph | (1, 6)-rook graph | (5, 6)-Harary graph | (6, 1)-arrangement graph | (6, 1)-Johnson graph | (6, 1)-Kneser graph | (6, 6)-Turán graph | 6-circulant graph (1, 2, 3) | ...

    (1, 6, 1)-honeycomb toroidal graph | 1-fusene graph 1 | (2, 2, 3)-Bouwer graph | (2, 3)-rook complement graph | (2, 6)-Harary graph | (3, 1)-bipartite Kneser graph | (3, 2)-arrangement graph | (3, 2)-permutation star graph | 3-Bruhat graph | 3-crown graph | ...

    Basic properties

    | vertex count | edge count | connected component count triangle graph | 3 | 3 | 1 square graph | 4 | 4 | 1 tetrahedral graph | 4 | 6 | 1 pentatope graph | 5 | 10 | 1 5-cycle graph | 5 | 5 | 1 5-wheel graph | 5 | 8 | 1 octahedral graph | 6 | 12 | 1 utility graph | 6 | 9 | 1 6-complete graph | 6 | 15 | 1 6-cycle graph | 6 | 6 | 1

    Common graph features

    biconnected | bridgeless | connected | cyclic | Hamiltonian | Harary | nonempty | simple | traceable

    Complement graph

    | complement graph name triangle graph | 3-empty graph square graph | 2-ladder rung graph tetrahedral graph | 4-empty graph pentatope graph | 5-empty graph 5-cycle graph | 5-cycle graph

    Dual graph

    | dual graph name tetrahedral graph | tetrahedral graph

    Line graph

    | line graph name triangle graph | triangle graph square graph | square graph tetrahedral graph | octahedral graph pentatope graph | 5-triangular graph 5-cycle graph | 5-cycle graph

    Topological properties

    | radius | diameter | girth triangle graph | 1 | 1 | 3 square graph | 2 | 2 | 4 tetrahedral graph | 1 | 1 | 3 pentatope graph | 1 | 1 | 3 5-cycle graph | 2 | 2 | 5 5-wheel graph | 1 | 2 | 3 octahedral graph | 2 | 2 | 3 utility graph | 2 | 2 | 4 6-complete graph | 1 | 1 | 3 6-cycle graph | 3 | 3 | 6 | vertex connectivity | edge connectivity triangle graph | 2 | 2 square graph | 2 | 2 tetrahedral graph | 3 | 3 pentatope graph | 4 | 4 5-cycle graph | 2 | 2 5-wheel graph | 3 | 3 octahedral graph | 4 | 4 utility graph | 3 | 3 6-complete graph | 5 | 5 6-cycle graph | 2 | 2

    Coloring properties

    | chromatic number | edge chromatic number triangle graph | 3 | 3 square graph | 2 | 2 tetrahedral graph | 4 | 3 pentatope graph | 5 | 5 5-cycle graph | 3 | 3 5-wheel graph | 3 | 4 octahedral graph | 3 | 4 utility graph | 2 | 3 6-complete graph | 6 | 5 6-cycle graph | 2 | 2

    Spectrum

    (-1)^2 2^1

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

    (-1)^3 3^1

    (-1)^4 4^1

    (1/2 (-1 - sqrt(5)))^2 (1/2 (-1 + sqrt(5)))^2 2^1

    (-2)^1 (1 - sqrt(5))^1 0^2 (1 + sqrt(5))^1

    (-2)^2 0^3 4^1

    (-3)^1 0^4 3^1

    (-1)^5 5^1

    (-2)^1 (-1)^2 1^2 2^1

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