Adjacency MatrixGraph DiameterComputational ComplexityIn this paper, a fast algorithm is proposed to calculate k{sup}(th) power of an n脳n Boolean matrix that requires O(kn{sup}3p) addition operations, where p is the probability that an entry of the matrix is 1. The algorithm generates a ...
The use of power sum symmetric functions leads to Newton's identities, which relate the traces of various powers of A, the adjacency matrix of a graph, and... H Werner,DCT Dirnberger,DCM Schulz - 《Angewandte Chemie International Edition》 被引量: 50发表: 1988年 Inversion-based hardware ...
Particular emphasis is given to the least eigenvalue of the adjacency matrix in the case of lexicographic powers of regular graphs, and to the algebraic connectivity and the largest Laplacian eigenvalues in the case of lexicographic powers of arbitrary graphs. This approach allows the determination ...
Adjacency matrixLaplacian matrixThis note deals with the relationship between the total number of k -walks in a graph, and the sum of the k -th powers of its vertex degrees. In particular, it is shown that the the number of all k -walks is upper bounded by the sum of the k -th ...
On the powers of tournament matricesVarious results are derived about the adjacency matrix of a tournament; in particular, it is shown that if a tournament T n is irreducible and n>-5, then its matrix is primitive with exponent at most n+2doi:10.1016/S0021-9800(67)80009-7J.W. Moon...
The Laplacian matrix of G is L(G) = D(G) A(G), where D(G) is the diagonal matrix of its vertex degrees and A(G) is the adjacency matrix. Let mu(1) >= mu(2) >= ... >= mu(n-1) >= mu(n) = 0 be the Laplacian eigenvalues of G. For a graph G and a real number...