ß-PARTITIONS, DETERMINANT AND PERMANENT OF GRAPHS

Let g be a graph (directed or undirected) having k number of blocks b1;b2 ,..., bk. a ß-partitionof g is a partition consists of k vertex-disjoint subgraph ( ^ b1; ^ b1; : : : ; ^ bk) such that ^bi is an induced subgraphof bi for і = 1; 2,..., k. the termsπ^ki=1 det(^bi);π^ki=1 per(^bi) represent the det-summands and the per-summands, respectively, corresponding to the b-partition (b^1;b^1,...,b^k). the determinant (permanent) ofa graph having no loops on its cut-vertices is equal to the summation of the det-summands (per-summands),corresponding to all possible ß-partitions. in this paper, we calculate the determinant and the permanent ofclasses of graphs such as block graph, block graph with negatives cliques, signed unicyclic graph, mixed completegraph, negative mixed complete graph, and star mixed block graphs.