graph_square (749B)
1 # Graph square 2 3 [graph_exponentiation] by 2 of [undirected_graph] 4 5 Some are [Hamiltonian]: [graph_square_hamiltonian] 6 7 Three variants: 8 - connecting vertices with a distance *at most* two: this is the usual notion of graph square 9 - [graph_square_root_problem] 10 - connecting vertices with a [walk] of length *exactly* two (but potentially also an edge): this is [graph_exact_square] 11 - connecting vertices with a distance *exactly* two: this is [graph_exact_distance_square] 12 13 The square of the [line_graph], and the [line_graph] of the square, are essentially always [Hamiltonian] for [connected_graphs], cf [nebesky1973line] 14 15 Up: [graph_exponentiation] 16 17 See also: [radoszewski2011hamiltonian], [graph_cube], [graph_square_root], [graph_exact_square]