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Some 50 employees joined Amplify. Desmos Studio was spun off as a separate public benefit corporation focused on building calculator products and other math tools. [7] In May 2023, Desmos released a beta for a remade Geometry Tool. In it, geometrical shapes can be made, as well as expressions from the normal graphing calculator, with extra ...
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal.
A connected graph G with the same vertex set as a connected hypergraph H is a host graph for H if every hyperedge of H induces a connected subgraph in G. For a disconnected hypergraph H, G is a host graph if there is a bijection between the connected components of G and of H, such that each connected component G' of G is a host of the ...
A Cartesian product of two graphs. In graph theory, the Cartesian product G H of graphs G and H is a graph such that: the vertex set of G H is the Cartesian product V(G) × V(H); and; two vertices (u,v) and (u' ,v' ) are adjacent in G H if and only if either u = u' and v is adjacent to v' in H, or; v = v' and u is adjacent to u' in G.
Clique-sums have a close connection with treewidth: If two graphs have treewidth at most k, so does their k-clique-sum.Every tree is the 1-clique-sum of its edges. Every series–parallel graph, or more generally every graph with treewidth at most two, may be formed as a 2-clique-sum of triangles.
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If Gaussian elimination applied to a square matrix A produces a row echelon matrix B, let d be the product of the scalars by which the determinant has been multiplied, using the above rules. Then the determinant of A is the quotient by d of the product of the elements of the diagonal of B : det ( A ) = ∏ diag ( B ) d . {\displaystyle \det ...
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