Slasti a strasti v životě matematika
Construction of Cospectral Integral Regular Graphs
Graphs G and H are called cospectral if they have the same characteristic polynomial. If eigenvalues are integral, then corresponding graphs are called integral graph. In this article we introduce a construction to produce pairs of cospectral integral regular graphs. Generalizing the construction of G4(a, b) and G5(a, b) due to Wang and Sun, we define graphs 𝒢4(G,H) and 𝒢5(G,H) and show that they are cospectral integral regular when G is an integral q-regular graph of order m and H is an integral...
Moore-Penrose inverse of a hollow symmetric matrix and a predistance matrix
By a hollow symmetric matrix we mean a symmetric matrix with zero diagonal elements. The notion contains those of predistance matrix and Euclidean distance matrix as its special cases. By a centered symmetric matrix we mean a symmetric matrix with zero row (and hence column) sums. There is a one-toone correspondence between the classes of hollow symmetric matrices and centered symmetric matrices, and thus with any hollow symmetric matrix D we may associate a centered symmetric matrix B, and vice...
The distance matrix of a bidirected tree.
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