Cycles and spanning trees
Copyright policy )Cycles and spanning trees
Given a connected graph \(G\), it is shown that the number of labelled spanning trees of \(G\) is equal to the determinant of a cycle-cycle incidence matrix. Using this cycle-based approach, it is seen that the graph of a convex polyhedron and its dual have the same number of spanning trees. The method can also be used to show that certain sequences of algebraic numbers can be represented by a recursive formula using only integers.
incidence matrix, adjacency matrix, Graphs and linear algebra (matrices, eigenvalues, etc.), Modelling and Simulation, cycles, algebraic numbers, Paths and cycles, spanning trees, Trees, Computer Science Applications
incidence matrix, adjacency matrix, Graphs and linear algebra (matrices, eigenvalues, etc.), Modelling and Simulation, cycles, algebraic numbers, Paths and cycles, spanning trees, Trees, Computer Science Applications
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