In a network of spin 12 particles, controlled through an external electro-magnetic field, the gyromagnetic ratio each is parameter that characterizes interaction with control field. Multipartite networks are such spins divided into subsets according to their and in one set interact same way all another set. Due presence symmetries these types systems, underlying Hilbert state space splits invar...

We present an explicit protocol E0 for faithfully teleporting an arbitrary two-qubit state via a genuine four-qubit entangled state. By construction, our four-partite state is not reducible to a pair of Bell states. Its properties are compared and contrasted with those of the four-party Greenberger-Horne-Zeilinger and W states. We also give a dense coding scheme D0 involving our state as a shar...

Let G be a multipartite multigraph without loops. Then G is said to be internally fair if its edges are shared as evenly as possible among all pairs of its partite sets. An internally fair factorization of G is an edge-decomposition of G into internally fair regular spanning subgraphs. A holey factor of G is a regular subgraph spanning all vertices but one partite set. An internally fair holey ...

In this paper, we introduce the class of k-partite episodes, which are time-series patterns of the form 〈A1, . . . , Ak〉 for sets Ai (1 ≤ i ≤ k) of events meaning that, in an input event sequence, every event of Ai is followed by every event of Ai+1 for every 1 ≤ i < k. Then, we present a backtracking algorithm Kpar and its modification Kpar2 that find all of the frequent k-partite episodes fro...

A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we give a useful sufficient and necessary condition for complete r-partite graphs to be integral, from which we can construct infinite many new classes of such integral graphs. It is proved that the problem of finding such integral graphs is equivalent to the problem of solving some Diophantin...

An edge dominating set in a graph G is a set of edges D such that every edge not in D is adjacent to an edge of D. An edge domatic partition of a graph C=(V, E) is a collection of pairwise-disjoint edge dominating sets of G whose union is E. The maximum size of an edge domatic partition of G is called the edge domatic number. In this paper, we study the edge domatic number of the complete parti...

We introduce a search problem for finding a regular bi-partite graph of maximum attainable girth for specified degree and number of vertices, by restricting the search space using a series of mathematically rigourous arguments from [1] and [2]. The goal of this paper is to derive the enumeration search algorithm for finding a girth maximum (m, r) BTU, which is notation for regular partite graph...

graph is called a complete r-partite graph if its vertex set can be partitioned into r independent sets V1, . . . , Vr such that for any i = 1, 2, . . . , r every vertex in Vi is adjacent to all other vertices in Vj , j 6= i. We denote a complete r-partite graph with part sizes |Vi| = ni by Kn1,...,nr . For a graph G and a positive integer k we use kG to denote k vertex-disjoint copies of G. Gi...

Nonclassical correlations between measurement results make entanglement the essence of quantum physics and the main resource for quantum information applications. Surprisingly, there are n-particle states which do not exhibit n-partite correlations at all but still are genuinely n-partite entangled. We introduce a general construction principle for such states, implement them in a multiphoton e...