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A convex hull of finitely many points in the Euclidean space Rd is known as a convex polytope. Graphically, they are planar graphs i.e. embeddable on R2. Minimum dominating sets possess diverse applications in computer science and engineering. Locating-dominating sets are a natural extension of dominating sets. Studying minimizing locating-dominating sets of convex polytopes reveal interesting distance-dominating related topological properties of these geometrical planar graphs. In this paper, exact value of the locating-dominating number is shown for one infinite family of convex polytopes. Moreover, tight upper bounds on γl−d are shown for two more infinite families. Tightness in the upper bounds is shown by employing an updated integer linear programming (ILP) model for the locating-dominating number γl−d of a fixed graph. Results are explained with help of some examples. The second part of the paper solves an open problem in Khan (2023) [28] which asks to find a domination-related parameter which delivers a correlation coefficient of ρ>0.9967 with the total π-electronic energy of lower benzenoid hydrocarbons. We show that the locating-dominating number γl−d delivers such a strong prediction potential. The paper is concluded with putting forward some open problems in this area.

The availability of industrial network topologies is limited, which presents a significant challenge for researchers in this field. Network generators are essential tools for generating realistic simulation outcomes in network research. Thus, it is crucial to use realistic topologies that can accurately represent the characteristics of the target network. The primary objective of this study is to address the existing research gap by developing an industrial network topology generator for novel topology datasets specific to industrial networks and the industrial Internet of Things (IIoT). In this paper, we describe the development of the graph theoretic industrial topology generator (GENIND), a topology generator that can produce realistic IIoT and industrial network topologies. The proposed GENIND network topology generator is validated through comparisons with real-world industrial network topologies. The evaluation framework assesses the performance of the proposed GENIND system using three main measures: the overall network structure, path-related factors, and resilience topological structure features. The results of the evaluation demonstrate a high degree of similarity between the graphs generated by the GENIND system and the real-world industrial networks used for comparison. This finding suggests that the generated graphs can be utilized as reliable tools to predict the behavior of industrial networks under various conditions.

Industrial networks, and more particularly, industrial control systems (ICSs) and industrial Internet of things (IIoT), are no longer isolated environments. The rapid increase of functional needs in Industry 4.0 has indeed exposed them to numerous cyberattacks. Cyberattacks against ICSs or IIoT can cause considerable societal and economic disruption. Cyber resilient and cybersecurity practices are essential to integrate secure networks, control systems, physical processes, and their interconnections toward handling cyberattacks. In this paper, we survey relevant cyber resilience strategies for industrial networks, focusing on ICSs and IIoT. First, we provide a coverage of resilient networks and the fundamental components of ICSs and IIoT. Second, state of the art articles that propose cyber resilience assessment frameworks are reviewed. They are classified according to the resilience aspects they address and the defense mechanism, anomaly detection, failure management and survivability strategy, as well as resilience measure they present. As a result, the main technical and human related challenges, practical limitations, and current cyber resilience needs of industrial networks are identified. Finally, we establish the principal requirements that cyber resilience schemes for industrial networks should meet shortly and suggest promising directions for future research.