Research Article A Robust Graph Theoretic Solution of Routing in Intelligent Networks Muhammad Aasim Qureshi, 1 Mohd Fadzil Hassan, 2 Muhammad Khurram Ehsan , 3 Muhammad Owais Khan, 4 Md YeaKub Ali , 5 and Shafiullah Khan 6 1 Department of Computer Sciences, Bahria University, Lahore Campus, Lahore, Pakistan 2 Computer and Information Science Department, University Teknologi, Petronas, Malaysia 3 Faculty of Engineering Sciences, Bahria University, Lahore Campus, Lahore, Pakistan 4 School of Systems and Technology, University of Management and Technology, Lahore, Pakistan 5 Department of Electronics and Telecommunication Engineering, Rajshahi University of Engineering & Technology (RUET), Rajshahi, Bangladesh 6 Department of Electronics, Islamia College University, Peshawar, Pakistan Correspondence should be addressed to Md YeaKub Ali; yeakub@ete.ruet.ac.bd Received 12 April 2022; Revised 20 May 2022; Accepted 3 June 2022; Published 20 June 2022 Academic Editor: Khaled Maaiuf Rabie Copyright © 2022 Muhammad Aasim Qureshi et al. This 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. Implementation of robust routing is very critical in network communication. Connecting devices like routers maintain databases for the whole network topology in the routing table. Each router needs to keep these tables updated with the best possible routes so that an efficient communication can always take place in nondelay tolerant intelligent networks that include military and tactical systems, vehicular communication networks, underwater acoustic networks, and intelligent sensor networks. The fast construction of shortest-path tree (SPT) is important to devise an efficient routing in a nondelay tolerant networks. That is why a simple and efficient algorithm is the need of the time. A robust routing solution SPT with OðV + EÞ time complexity is proposed to supersede the existing landmark. 1. Introduction Network routing is a backbone of intelligent communication networks specifically nondelay tolerant networks that include military and tactical systems, vehicular communica- tion networks (VCNs), underwater acoustic networks (UANs), and intelligent sensor networks (ISNs) to send the communication data between vertices in a certain network. For the purpose, every router maintain routing tables. These tables manage routes of various network destinations. This network routing process is generally accomplished based on these routing tables and routes defined in them. This makes the formation, written in a memory of these routers, critically important for successful and efficient routing. There exist many graph theoretic solutions of this routing problem. In a network, the vertex of a graph represents a router, and edge/link which connect these vertices represents physical links between the routers. The needs for broadband Internet applications have increased rapidly in today’s Internet. Which makes high speed routing inevitable and has become the key at open shortest-path first (OSPF). As a result of topological changes that take place due to due to an unavoidable circumstances at the OSPF, these algorithms update the routing table to handle the new topological changes. For example, if some link fails in a network, then there is no way but to recalculate these paths [1]. In such scenarios, these shortest paths are regenerated by running the algorithms again [2]. We can formally define shortest-path problem as follows: Hindawi Wireless Communications and Mobile Computing Volume 2022, Article ID 9661411, 7 pages https://doi.org/10.1155/2022/9661411