Research Article Irregularity of Block Shift Networks and Hierarchical Hypercube Networks Juanyan Fang, 1 Iftikhar Ahmed , 2,3 Abid Mehboob, 4 Kashif Nazar, 2 and Haseeb Ahmad 2,5 1 Institute of Information Technology & Engineering Management, Tongling College, Tongling 244000, China 2 Department of Mathematics, COMSATS University Islamabad, Lahore 54000, Pakistan 3 Department of Mathematics, Riphah International University, Lahore 54000, Pakistan 4 Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan 5 Department of Mathematics, Lahore Leads University, Lahore, Pakistan Correspondence should be addressed to Iftikhar Ahmed; iffi6301@gmail.com Received 20 October 2019; Accepted 21 November 2019; Published 18 December 2019 Guest Editor: Jia-Bao Liu Copyright © 2019 Juanyan Fang et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ere is extremely a great deal of mathematics associated with electrical and electronic engineering. It relies upon what zone of electrical and electronic engineering; for instance, there is much increasingly theoretical mathematics in communication theory, signal processing and networking, and so forth. Systems include hubs speaking with one another. A great deal of PCs connected together structure a system. Mobile phone clients structure a network. Networking includes the investigation of the most ideal method for executing a system. Graph theory has discovered a significant use in this zone of research. In this paper, we stretch out this examination to interconnection systems. Hierarchical interconnection systems (HINs) give a system to planning systems with diminished connection cost by exploiting the area of correspondence that exists in parallel applications. HINs utilize numerous levels. Lower-level systems give nearby correspondence, while more significant level systems encourage remote correspondence. HINs provide issue resilience within the sight of some defective nodes and additionally interfaces. Existing HINs can be comprehensively characterized into two classes: those that use nodes or potential interface replication and those that utilize reserve interface nodes. 1. Introduction Graph theory has many applications in chemistry, physics, computer sciences, and other applied sciences [1–9]. Multi- processor interconnection networks (MINs) are required to connect processor-memory pairs, each of which is known as the processing node. Design and usage of MINs have gained remarkable attention because of the availability of powerful microprocessors and memory chips and also due to its low cost [10, 11]. Hierarchical interconnection network (HIN) [12] is a framework for designing new networks that decrease link cost and has applications in parallel communications. e multistage networks have applications as communication networks for parallel computing [12–14]. For details about graph theory, we recommend the references [15–19]. roughout this article, all graphs are finite, undirected, and simple. Let G �(V(G),E(G)) be such a graph with vertex set V(G) and edge set E(G). e order of G is the cardinality of its vertex set, and size is the cardinality of its edge set. In a network, the vertices of G correspond to node, and an edge between two vertices is the link between these vertices. e degree of a vertex u of a graph G is symbolized by d u and is defined as the number of edges incident with u. A graph is said to be regular, if all its vertices have the same degree; otherwise, it is irregular. For the first time in history, Chartrand et al. [20] underlined the study of irregular graphs. From that point forward, the irregularity degree and irregular graphs have turned into the essential open issue of graph theory. A graph is said to be a perfect graph if all the vertices have different Hindawi Journal of Chemistry Volume 2019, Article ID 1042308, 12 pages https://doi.org/10.1155/2019/1042308