Cloud computing has become essential to various application services, requiring robust data center networks (DCNs) to support its infrastructure. This paper explores the establishment of a three-party proprietary communication channel and its related applications in a highly scalable data center network (HSDC). This novel research topic involves third-party authentication (TPA) in cloud applications. With the increasing demand for secure and reliable communication, we investigate the implementation of internally disjoint 3-Steiner paths (ID-3SPs), which facilitate message transmission with the involvement of a trusted third party. By explicitly constructing ID-3SPs and developing a definitive algorithm, we incorporate 3-path connectivity with TPA-related applications to enhance transmission efficiency caused by multi-paths while ensuring fault tolerance in the event of network component failures. Extensive experiments conducted in HSDC have shown that our findings significantly improve the reliability and efficiency of communication in DCNs, demonstrating their potential for practical applications that will benefit diverse fields, ranging from e-commerce to supply chains.

In this paper, we determine the wide diameters of regular hyper-stars HS(2k,k) and folded hyper-stars FHS(2k,k)⁠. We first provide a connection between the wide diameter and the maximum height of a set of particular spanning trees, called independent spanning trees (ISTs for short), of a graph. According to this relation, we analyze the heights of ISTs constructed in the previous works to establish upper bounds of the wide diameters of HS(2k,k) and FHS(2k,k)⁠. By contrast, we take the known results of fault diameters of HS(2k,k) and FHS(2k,k) as lower bounds. Consequently, we obtain the following results: (i) Dw(HS(2k,k))=2k+1 for k≥2⁠, and (ii) Dw(FHS(4,2))=3 and Dw(FHS(2k,k))=k+2 for k≥3⁠, where Dw(G) stands for the wide diameter of a graph G. The latter gives the answer of a question arisen from a previous work [(2015) Pruning longer branches of ISTs on folded hyper-stars, Comput. J., 58, 2972–2981]. In addition, we ascertain that all ISTs of HS(2k,k) and FHS(2k,k) constructed in the previous works are optimal in the sense that their heights are minimized.

Hypercubes and star graphs are widespread topologies of interconnection networks. The class of hyper-stars was introduced as a new type of interconnection network to compete with both hypercubes and star graphs, and the class of folded hyper-stars is a strengthened variation of hyper-stars with additional links to connect nodes with complemented 0/1-strings. Constructing independent spanning trees (ISTs) has numerous applications in networks such as fault-tolerant broadcasting and secure message distribution. Recently, Yang and Chang [IST on folded hyper-stars, Networks 56 (2010), 272–281] proposed an algorithm to construct |$k+1$| ISTs on folded hyper-star |$FHS(2k,k)$|⁠. For |$k\geqslant 4$|⁠, their constructions include |$k$| ISTs with a height |$2k-2$| and the other one with a height |$k+1$|⁠. In this paper, we refine their constructed rules on |$FHS(2k,k)$| for |$k\geqslant 3$| and provide a set of constructions including |$k$| ISTs with a height |$k+2$| and the other one with a height |$k+1$|⁠. As a by-product, we obtain an improvement on the upper bound of the fault diameter (respectively, the wide diameter) of |$FHS(2k,k)$|⁠.

The use of multiple independent spanning trees (ISTs) for data broadcasting in networks provides a number of advantages, including the increase of fault-tolerance, bandwidth and security. Thus, the designs of multiple ISTs on several classes of networks have been widely investigated. In this paper, we give an algorithm to construct ISTs on enhanced hypercubes Qn,k, which contain folded hypercubes as a subclass. Moreover, we show that these ISTs are near optimal for heights and path lengths. Let D(Qn,k) denote the diameter of Qn,k. If n - k is odd or n - k ∈ {2; n}, we show that all the heights of ISTs are equal to D(Qn,k) + 1, and thus are optimal. Otherwise, we show that each path from a node to the root in a spanning tree has length at most D(Qn,k) + 2. In particular, no more than 2.15 percent of nodes have the maximum path length. As a by-product, we improve the upper bound of wide diameter (respectively, fault diameter) of Qn,kfrom these path lengths.

A set of k spanning trees rooted at the same vertex r in a graph G is called independent [and the trees are called independent spanning trees (ISTs)] if, for any vertex x ≠ r, the k paths from x to r, one path in each tree, are internally disjoint. The design of ISTs on graphs has applications to fault-tolerant broadcasting and secure message distribution in networks. It was conjectured that, for any k-connected graph, there exist k ISTs rooted at any vertex of the graph. The conjecture has been proved true for k-connected graphs with k ≤ 4, and remains open otherwise. In this paper, we deal with the problem of constructing ISTs on the Cartesian product of a sequence of hybrid graphs, including cycles and complete graphs. Consequently, this result generalizes a number of previous works. Moreover, the construction is shown to be optimal in the sense that the heights of ISTs are minimized.

Abstract Fault‐tolerant broadcasting and secure message distribution are important issues for numerous applications in networks. It is a common idea to design multiple independent spanning trees (ISTs) as a broadcasting scheme or a distribution protocol for receiving high levels of fault‐tolerance and security. Recently, hyper‐stars were introduced as a competitive model of interconnection network for both hypercubes and star graphs. The class of folded hyper‐stars is a strengthened variation of hyper‐stars obtained by adding additional links to connect complemented nodes. Both hyper‐stars and folded hyper‐stars have been shown to have lower network cost (measured by the product of degree and diameter) than hypercubes, folded hypercubes, and other variants. In this article, we propose an algorithm to construct k + 1 ISTs on a regular folded hyper‐star FHS (2k,k), where the number of ISTs matches the connectivity of FHS(2k,k). In particular, for k > 4, the constructed k ISTs have height 2 k − 2, and the other one has height k + 1. © 2010 Wiley Periodicals, Inc. NETWORKS, 2010

Two spanning trees rooted at vertex r in a graph G are called independent spanning trees (ISTs) if for each vertex v in G, vner, the paths from vertex v to vertex r in these two trees are internally distinct. If the connectivity of G is k, the IST problem is to construct k ISTs rooted at each vertex. The IST problem has found applications in fault-tolerant broadcasting, but it is still open for general graphs with connectivity greater than four. In this paper, we shall propose a very simple algorithm for solving the IST problem on multidimensional torus networks. In our algorithm, every vertex can determine its parent for a specific independent spanning tree only depending on its own label. Thus, our algorithm can also be implemented in parallel systems or distributed systems very easily.

Abstract Jwo et al. [Networks 23 (1993) 315–326] introduced the alternating group graph as an interconnection network topology for computing systems. They showed that the proposed structure has many advantages over n‐cubes and star graphs. For example, all alternating group graphs are hamiltonian‐connected (i.e., every pair of vertices in the graph are connected by a hamiltonian path) and pancyclic (i.e., the graph can embed cycles with arbitrary length with dilation 1). In this article, we give a stronger result: all alternating group graphs are panconnected, that is, every two vertices x and y in the graph are connected by a path of length k for each k satisfying d(x, y) ≤ k ≤ |V| − 1, where d(x, y) denotes the distance between x and y, and |V| is the number of vertices in the graph. Moreover, we show that the r‐dimensional alternating group graph AGr, r ≥ 4, is (r − 3)‐vertex fault‐tolerant Hamiltonian‐connected and (r − 2)‐vertex fault‐tolerant hamiltonian. The latter result can be viewed as complementary to the recent work of Lo and Chen [IEEE Trans. Parallel and Distributed Systems 12 (2001) 209–222], which studies the fault‐tolerant hamiltonicity in faulty arrangement graphs. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(4), 302–310 2004