Fibonacci-Weighted Lexicographic Product of Open Neighborhood Graphs for Smart IoT Optimization
Abstract
The paper has determined that the optimizing networks in Smart City IoT systems by application of Fibonacci-weighted Lexicographic Product Graphs. The emphasis is put on the regular graphs and their associated Open Neighborhood Graphs. The research uses the Fibonacci edge weight on different graphs, regular, cycle, complete and others by application of lexicographic products graphs. It looks at major graph features like the degree of the vertices, the structure of the edges and the weights of the all the edges which are computed through the use of the Fibonacci sequences. These graph models are easy to generate and visualize with the help of the given MATLAB codes, as well as help to create more efficient communication structures. This technique used to monitor the environment between Smart Cities incidentally improves fault tolerance, reduces energy consumption, and improves the usefulness of communication in large-scale internet of things systems.
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References
[2] P. Schweitzer, Iterated open neighborhood graphs and generalizations, Discrete Appl. Math., 161 (2013), 1150–1162.
[3] R. Govindaraju, M. S. Krishnamoorthy, N. Deo, Fibonacci Networks, Fibonacci Q., 32(4) (1994), 325–334.
[4] P. Ferrer-Cid, J. García-Garreta, A. Cuzzocrea, Graph-powered data quality in IoT monitoring platforms, J. Netw. Comput. Appl., 2025.
[5] I. Dey, N. Marchetti, Optimized Topology Control for IoT Networks, arXiv:2410.03204, 2024.
[6] K. Akrida, et al., General position problems in strong and lexicographic products, arXiv:2408.15951, 2024.
[7] A. Ahadi, O. Giménez, M. Siggers, Fibonacci-run graphs I: Basic properties, Discrete Appl. Math., 305 (2021), 1–21.
[8] G. Bhatnagar, A weighted extension of Fibonacci numbers, Preprint, 2023.
[9] R. B. Prasad, A. M. Reddy, Edge properties of lexicographic product graphs of open neighborhood graphs, Sci. Temper, 2025.
[10] S. Canoy Jr., J. Dalasing, The Neighborhood Graph of a Graph, Preprint, 2015.
[11] M. Zaman, N. Hossain, S. M. Liton, A Review of IoT-Based Smart City Development and Management, Smart Cities, 7(3) (2024), 61.
[12] Z. Wang, H. Chen, A Survey on Knowledge-Graph Research in Smart Cities, ACM Comput. Surv., 2024.
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