Closed-form topological and spectral invariants for periodic ladder-based vibration networks

Suleiman Ibrahim Mohammad
Department of Business Administration, Business School, Al al-Bayt University, Mafraq 25113, Jordan; Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Yogeesh Nijalingappa
Mathematics & Natural Sciences, Gulf University for Science & Technology, Safat 13060, Kuwait
Asokan Vasudevan
Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
P. William
School of Computer Science and Technology, Karunya Institute of Technology and Sciences (Deemed University), Coimbatore 641114, India; Centre for Research and Consultancy, UNITAR International University, Petaling Jaya 47301, Malaysia
Jonathan Lee
Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Tarun Madan Kanade
Symbiosis Institute of Operations Management, Symbiosis International (Deemed University), Nashik 422008, India
Mohammad Faleh Ahmmad Hunitie
Department of Public Administration, School of Business, University of Jordan, Amman 11942, Jordan

Article ID: 4498

Keywords: ladder network; cylindrical ladder; Sombor index; reduced Sombor coindex; eccentric connectivity index; Wiener index; graph energy

Abstract

This paper investigates two closely related network families, the open ladder graph and the cylindrical ladder graph, as exact test beds for degree-based, eccentricity-based, distance-based, and spectral descriptors. The two graphs can be seen as graph-theoretic two-rail models with and without periodic closure, allowing an exact comparison boundary effects versus cyclic-closure-effect. We obtain closed expressions for the Sombor index, reduced Sombor index, Sombor coindex, reduced Sombor coindex, first and second Zagreb indices, forgotten index, Randić index geometric-arithmetic index atom-bond connectivity index total eccentricity average eccentricity eccentric connectivity index Wiener Index radius diameter and total π-electron energy. For the energy part, we derive exact spectral sums and trigonometric closed forms using the Cartesian-product spectra of the underlying path and cycle graphs. Numerical tables and plots show that periodic closure increases all degree-regularity descriptors while sharply decreasing distance descriptors. In contrast, the total π-electron energy changes only by a small oscillatory amount, and both families share the same asymptotic energy density. The adjacency-based energy indeed can be interpreted explicitly as graph energy, instead of mechanical vibrational energy. An additional mass-spring formulation rooted on the graph Laplacian provides the analog equations of motion, natural-frequency spectra, dispersion samples and frequency-response operator for those analogous ladder topologies.

Published

2026-07-27

How to Cite

Mohammad, S. I., Nijalingappa, Y., Vasudevan, A., William, P., Lee, J., Kanade , T. M., & Hunitie, M. F. A. (2026). Closed-form topological and spectral invariants for periodic ladder-based vibration networks. Sound & Vibration, 60(5). https://doi.org/10.59400/sv4498

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Vol. 60 No. 5 (2026): In Progress

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Closed-form topological and spectral invariants for periodic ladder-based vibration networks

Abstract

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