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  2. Strongly regular graph - Wikipedia

    en.wikipedia.org/wiki/Strongly_regular_graph

    Following the terminology in much of the strongly regular graph literature, the larger eigenvalue is called r with multiplicity f and the smaller one is called s with multiplicity g. Since the sum of all the eigenvalues is the trace of the adjacency matrix , which is zero in this case, the respective multiplicities f and g can be calculated:

  3. Nullity (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Nullity_(graph_theory)

    If the graph has n vertices and m edges, then: In the matrix theory of graphs, the nullity of the graph is the nullity of the adjacency matrix A of the graph. The nullity of A is given by n − r where r is the rank of the adjacency matrix. This nullity equals the multiplicity of the eigenvalue 0 in the spectrum of the adjacency matrix. See ...

  4. Bézout's theorem - Wikipedia

    en.wikipedia.org/wiki/Bézout's_theorem

    The resultant R(x,t) of P and Q with respect to y is a homogeneous polynomial in x and t that has the following property: (,) = with (,) (,) if and only if it exist such that (,,) is a common zero of P and Q (see Resultant § Zeros).

  5. Multiplicity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Multiplicity_(mathematics)

    Graph of x 3 + 2x 2 − 7x + 4 with a simple root (multiplicity 1) at x=−4 and a root of multiplicity 2 at x=1. The graph crosses the x axis at the simple root. It is tangent to the x axis at the multiple root and does not cross it, since the multiplicity is even. The graph of a polynomial function f touches the x-axis at the real roots of ...

  6. Resolvent cubic - Wikipedia

    en.wikipedia.org/wiki/Resolvent_cubic

    Graph of the polynomial function x 4 + x 3 – x 2 – 7x/4 – 1/2 (in green) together with the graph of its resolvent cubic R 4 (y) (in red). The roots of both polynomials are visible too. In algebra, a resolvent cubic is one of several distinct, although related, cubic polynomials defined from a monic polynomial of degree four:

  7. Laplacian matrix - Wikipedia

    en.wikipedia.org/wiki/Laplacian_matrix

    In the matrix notation, the adjacency matrix of the undirected graph could, e.g., be defined as a Boolean sum of the adjacency matrix of the original directed graph and its matrix transpose, where the zero and one entries of are treated as logical, rather than numerical, values, as in the following example:

  8. Intersection number - Wikipedia

    en.wikipedia.org/wiki/Intersection_number

    Let X be a Riemann surface.Then the intersection number of two closed curves on X has a simple definition in terms of an integral. For every closed curve c on X (i.e., smooth function :), we can associate a differential form of compact support, the Poincaré dual of c, with the property that integrals along c can be calculated by integrals over X:

  9. Resolution of singularities - Wikipedia

    en.wikipedia.org/wiki/Resolution_of_singularities

    Let X be the subvariety of the four-dimensional affine plane, with coordinates x,y,z,w, generated by y 2-x 3 and x 4 +xz 2-w 3. The canonical desingularization of the ideal with these generators would blow up the center C 0 given by x=y=z=w=0. The transform of the ideal in the x-chart if generated by x-y 2 and y 2 (y 2 +z 2-w 3).