High-fidelity quantum state transfer is critical for communication and scalable computation. Current algorithms on the complete bipartite graph, which are based discrete-time walk search algorithms, suffer from low fidelity in some cases. To solve this problem, paper we propose a two-stage algorithm graph. The achieved by generalized Grover with one marked vertex. walk’s coin operators query or...

Given a finite connected bipartite graph B = (X, Y ) we consider the simplicial complexes of complete subgraphs of the square B of B and of its induced subgraphs B[X] and B[Y ]. We prove that these three complexes have isomorphic fundamental groups. Among other applications, we conclude that the fundamental group of the complex of complete subgraphs of a graph G is isomorphic to that of the cli...

Let $ G=(V,E) be a graph. The double vertex graph $F_2(G)$ of G is the whose set consists all 2 $-subsets V(G) such that two vertices are adjacent in F_2(G) if their symmetric difference pair $. super--connectivity connected minimum number removal results disconnected without an isolated vertex. In this paper, we determine complete bipartite K_{m,n} for m\geq 4 where n\geq m+2

Let G be a graph and H a subgraph of G. A D(G,H, λ) design is a collection D of subgraphs of G each isomorphic to H so that every 2-path (path of length 2) in G lies in exactly λ subgraphs in D. The problem of constructing D(Kn, Cn, 1) designs is the so-called Dudeney’s round table problem. We denote by Ck a cycle on k vertices and by Pk a path on k vertices. In this paper, we construct D(Kn,n,...

We report on the phase transition of finding a complete subgraph, of specified dimensions, in a bipartite graph. Finding a complete subgraph in a bipartite graph is a problem that has growing attention in several domains, including bioinformatics, social network analysis and domain clustering. A key step for a successful phase transition study is identifying a suitable order parameter, when non...

The k-chain subgraph cover problem asks if the edge set of a given bipartite graph G is the union of the edge sets of k chain graphs, where each chain graph is a subgraph of G. Although the X--chain subgraph cover problem is known to be NP-complete for the class of bipartite graphs, it is still unknown whether this problem is NP-complete or polynomial-time solvable for subclasses of bipartite g...

A complete classification is given of vertex primitive and vertex bi-primitive s-arc regular graphs with s ≥ 3. In particular, it is shown that the Petersen graph and Coxeter graph are the only vertex primitive 3-arc regular graphs, and that vertex bi-primitive 3-arc regular graphs consist of the complete bipartite graph K3,3, the standard double covers of the Petersen graph and Coxeter graph, ...