Combinatorial Matrix Theory
Cambridge University Press, Jul 26, 1991 - Mathematics - 367 pages
This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of matrices viewed as arrays of numbers rather than algebraic objects in themselves.
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0,l)-matrix of order adjacency matrix algebraic algorithm Amer apply assume bipartite graph Cayley table color column sum vector combinatorial complete graph configuration contains Corollary decomposition define denote determinant diagonal hypergraphs digraph D(A directed cycle divisor edges of G eigenvalues exists exponent following theorem fully indecomposable matrix graph G graph of order Graph Theory Hence hypergraphs implies incidence matrix integer irreducible matrix isomorphism l)-matrix latin rectangle Lemma length Let G Linear Alg main diagonal Math matrix of order mutually orthogonal latin n-set nearly reducible nonnegative integral matrix nonnegative matrix nonzero diagonal nonzero elements number of 1's orthogonal latin squares outdegree partial latin square partition per(A perfect matching permanent permutation matrix polynomial positive integer primitive matrix Proof Prove row sum vector satisfies sequence sign-nonsingular square of order strong component strongly connected strongly regular graph subgraph submatrix subpermutation matrices subsets Suppose symmetric term rank transversal vertex vertex set