Acyclic Matrices of Zeros and Ones

  title={Acyclic Matrices of Zeros and Ones},
  author={Richard A. Brualdi and E. S. Solheid},
Let A = [ao] be an n x n (0, 1)-matrix, that is, a matrix all of whose entries are zeros and ones. Associated with A there are two bipartite graphs Go(A) and GI(A) whose edges correspond respectively to the O's and the l ' s of A. The graph GI(A) has 2n vertices xl , . • • , xn (row vertices) and Yl, . . . , Yn (column vertices), where there is an edge joining xi and Yi if and only if a o = 1 (1 ~< i, j <n). Le t .In be the n x n matrix of all l ' s . Then the graph Go(A) is defined by G o ( A… CONTINUE READING