Fujishige proposed a polynomial-time maximum flow algorithm using maximum adjacency (MA) orderings. Computational results by Fujishige and Isotani showed that the algorithm was slower in practice than Goldberg and Tarjan’s algorithm. In this paper we propose an improved version of Fujishige’s algorithm using preflows. Our computational results show that the improved version is much faster than ...

A square (0, 1)-matrix X of order n ≥ 1 is called fully indecomposable if there exists no integer k with 1 ≤ k ≤ n− 1, such that X has a k by n− k zero submatrix. The reduced adjacency matrix of a bipartite graph G = (A,B,E) (having A ∪ B = {a1, ..., am} ∪ {b1, ..., bn} as vertex set, and E as edge set), is X = [xij ], 1 ≤ i ≤ m, 1 ≤ j ≤ n, where xij = 1 if aibj ∈ E and xij = 0 otherwise. A sta...

We have developed simple algorithms that allow adjacency and proximity searching in Google and the Science Citation Index (SCI). The SCI algorithm exploits the fact that SCI stopwords in a search phrase function as a placeholder. Such a phrase serves effectively as a fixed adjacency condition determined by the number n of adjacent stopwords (i.e., retrieve all records where word A and word B ar...

For an undirected graph without self-loop, we prove: (i) that the number of closed patterns in the adjacency matrix of is even; (ii) that the number of the closed patterns is precisely double the number of maximal complete bipartite subgraphs of ; (iii) that for every maximal complete bipartite subgraph, there always exists a unique and distinct pair of closed patterns that matches the two vert...

Let G be a k-degenerate graph of order n. It is well-known that G has no more edges than Sn,k, the join of a complete graph of order k and an independent set of order n−k. In this note, it is shown that Sn,k is extremal for some spectral parameters of G as well. More precisely, letting μ (H) and q (H) denote the largest eigenvalues of the adjacency matrix and the signless Laplacian of a graph H...

Let Γ=(V,E) be a graph and ‎W_(‎a)={w_1,…,w_k } be a subset of the vertices of Γ and v be a vertex of it. The k-vector r_2 (v∣ W_a)=(a_Γ (v,w_1),‎…‎ ,a_Γ (v,w_k)) is the adjacency representation of v with respect to W in which a_Γ (v,w_i )=min{2,d_Γ (v,w_i )} and d_Γ (v,w_i ) is the distance between v and w_i in Γ. W_a is called as an adjacency resolving set for Γ if distinct vertices of ...

We give quantum algorithms and quantum lower bounds for computing a maximal and a maximum independent. We present applications of these algorithms for some graph problems. Our results improve the best classical complexity bounds for the corresponding problems. Quantum Graph Algorithms We consider two models for the represention of graphs G = (V,E) with V = {v1, . . . , vn}: •Adjacency matrix model