LAUSR

Computing the permanent of a (0, 1)-square matrix is a $$\# P$$ # P -complete problem, whereas the determinant and rank are solved in polynomial time. A simple graph is called a bi-block graph if each block in it is a complete bipartite graph. In this paper, we consider the (0, 1)-adjacency matrix of a bi-block to find its permanent, determinant, and rank. These numbers are known for trees, so this work is a generalization of the results on trees. To compute the permanent and determinant we define two partitions namely block bipartite vertex covering and block edge perfect matching which are computable in linear time. For the rank, we give a linear time algorithm.