Reliability Evaluation of Augmented Cubes on Degree

The [Formula: see text]-dimensional augmented cube [Formula: see text], proposed by Choudum and Sunitha in 2002, is one of the most famous interconnection networks of the distributed parallel system. Reliability evaluation of underlying topological structures is vital for fault tolerance analysis of this system. As one of the most extensively studied parameters, the [Formula: see text]-conditional edge-connectivity of a connected graph [Formula: see text], [Formula: see text], is defined as the minimum number of the cardinality of the edge-cut of [Formula: see text], if exists, whose removal disconnects this graph and keeps each component of [Formula: see text] having minimum degree at least [Formula: see text]. Let [Formula: see text], [Formula: see text] and [Formula: see text] be three integers, where [Formula: see text], if [Formula: see text] and [Formula: see text], if [Formula: see text]. In this paper, we determine the exact value of the [Formula: see text]-conditional edge-connectivity of [Formula: see text], [Formula: see text] for each positive integer [Formula: see text] and [Formula: see text], and give an affirmative answer to Shinde and Borse’s corresponding conjecture on this topic in [On edge-fault tolerance in augmented cubes, J. Interconnection Netw. 20(4) (2020), DOI:10.1142/S0219265920500139].

Fault Tolerance of Optical Hypercube Interconnection Networks with r -Communication Pattern

As power grids and optical interconnection networks are interdependent, the reliabilities of the optical networks are critical issues in power systems. The optical networks hold prominent performance including wide bandwidth, low loss, strong anti-interference capability, high fidelity, and reliable performance. They are regarded as promising alternatives to electrical networks for parallel processing. This paper is aimed at taking the first step in understanding the communication efficiencies of optical networks. For that purpose, on optical networks, we propose a series of novel notions including communication pattern, r -communication graph, reduced diameter, enhanced connectivity, r -diameter, and r -connectivity. Using these notions, we determine that the r -diameter and r -connectivity of the optical n -dimensional hypercube network are n / r and n 1 + n 2 + ⋯ + n r , respectively. Since the parameter r is variable, we can adjust different values of r on the basis of the wavelength resources and load of the optical networks, achieving enhanced communication efficiencies of these networks. Compared with the electric n -dimensional hypercube network, the proposed communication pattern on the optical hypercube network not only reduces the maximum communication delay of the conventional electrical hypercube significantly but also improves its fault tolerance remarkably.

Special Issue on Networks-on-Chip Again on the Rise: From Emerging Applications to Emerging Technologies

Twenty years after the advent of interconnection networks to tackle the on-chip communication bottleneck [...]

Intuitionistic fuzzy incidence graphs

Connectivity parameters have a crucial role in the study of different networks in the physical world. The notion of connectivity plays a key role in both theory and application of different graphs. In this article, a prime idea of connectivity concepts in intuitionistic fuzzy incidence graphs (IFIGs) with various examples is examined. IFIGs are essential in interconnection networks with influenced flows. Therefore, it is of paramount significance to inspect their connectivity characteristics. IFIGs is an extended structure of fuzzy incidence graphs (FIGs). Depending on the strength of a pair, this paper classifies three different types of pairs such as an α - strong, β - strong, and δ-pair. The benefit of this kind of stratification is that it helps to comprehend the fundamental structure of an IFIG thoroughly. The existence of a strong intuitionistic fuzzy incidence path among vertex, edge, and pair of an IFIG is established. Intuitionistic fuzzy incidence cut pairs (IFICPs) and intuitionistic fuzzy incidence trees (IFIT) are characterized using the idea of strong pairs (SPs). Complete IFIG is defined, and various other structural properties of IFIGs are also investigated. The proof that complete IFIG does not contain any δ-pair is also provided. A real-life application of these concepts related to the network of different computers is also provided.

The l-good-neighbor edge connectivity of graphs

The l -good-neighbor edge connectivity is an useful parameter to measure the reliability and tolerance of interconnection networks. For a graph H with order p and an integer l (l ≥ 0), an edge subset X ⸦ E(H) is called a l-good-neighbor edge-cut if H − X is disconnected and the minimum degree of every component of H − X is at least £. The order of the minimum l-good-neighbor edge-cut of H is called the l-good-neighbor edge connectivity of H, denoted by λ l (H). In this paper, we show λ(H) ≤ λ l+1(H), obtain the bounds of λl (H) when 0 ≤ l ≤ [p-2/2], character some graphs with the small λl (H) and get some results about the Erdös-Gallai-type problem about λl (H).

A Novel Tradeoff Analysis between Traffic Congestion and Packing Density of Interconnection Networks for Massively Parallel Computers

From disaster prevention to mitigation, drug analysis to drug design, agriculture to food security, IoT to AI, and big data analysis to knowledge or sentiment mining, a high computation power is a prime necessity at present. As such, massively parallel computer (MPC) systems comprising a large number of nodes are gaining popularity. To interconnect these huge numbers of nodes efficiently, hierarchical interconnection networks are an attractive and feasible option. A Tori-connected flattened butterfly network (TFBN) has been proposed by the authors in a prior work for future generation MPC systems. In the previous study, the static network performance and static cost-effectiveness were evaluated. In this research, a novel trade-off factor named message traffic congestion vs. packing density trade-off factor has been proposed, which characterizes the message congestion in the network and its packing density. The factor is used to statically assess the suitability of the implementation of an interconnection network. The message traffic density, packing density, and new factor have been evaluated for the proposed network and similar competitive networks such as TTN, TESH, 2D-Mesh, 3D-Mesh, 2D-Torus, and 3D-Torus. It has been found that the performance of the TFBN is superior to the other networks.