Ev-Degree and Ve-Degree Based Topological Indices for Network Analysis

Aneela Aslam; Muhammad Danial Faiz; Mukhtar Ahmad Ahmad; Roslan Hasni; Ather Qayyum

doi:10.5269/bspm.78682

Aneela Aslam Department of Mathematics, University of Southern Punjab Multan, Pakistan
Muhammad Danial Faiz Department of Mathematics, University of Southern Punjab Multan, Pakistan
Mukhtar Ahmad Ahmad Khawja Fareed University of Engineering and Information Technology Rahim Yar Khan
Roslan Hasni Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu 21030 Kuala Nerus, Terengganu, Malaysia
Ather Qayyum Institute of Mathematical Sciences, Universiti Malaya, Malaysia

Resumen

Topological indices are essential tools for the quantitative characterization of complex networks, with wide-ranging applications in chemistry, biology, and computer science. Among these, ev-degree and ve-degree based indices have emerged as effective measures for capturing structural properties of graphs. In this work, we introduce and compute new classes of hyper ve-degree, polynomial ve-degree, and hyper-polynomial ve-degree indices, together with their generalized first-, second-, and third-order forms for amytose and cyclodextrin networks. Furthermore, the ev-degree Randic index and harmonic topological indices are derived and analyzed. To validate the proposed approach, three-dimensional graphical visualizations are generated using \textsc{Maple} software. The findings demonstrate that these indices not only enrich chemical graph theory but also provide deeper insights into the structural and biological characteristics of chemical compounds, thereby strengthening their significance in network science and related disciplines.

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Citas

[1] West, D. B. (2001). Introduction to Graph Theory. Prentice Hall.
[2] Gutman, I., & Polansky, O. E. (2002). Mathematical Concepts in Organic Chemistry: Topological Indices. Springer.
[3] Estrada, E. (2012). The Structure of Complex Networks: Theory and Applications. OxfordUniversity Press.
[4] Gutman, I., & Trinajsti´c, N. (1972). Graph theory and molecular orbitals. Croatica ChemicaActa, 45, 209–219.
[5] Randi´c, M. (1975). Characterization of molecular branching. Journal of the American Chemical Society, 97(23), 6609–6615.
[6] Estrada, E. (1998). Atomic branching in molecules. Chemical Physics Letters, 287(1–2),67–75.
[7] Vuki´cevi´c, D., & Furtula, B. (2009). Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges. Journal of Mathematical Chemistry, 46,1369–1376.
[8] Chellali, M., Favaron, O., Hansberg, A., & Volkmann, L. (2018). Edge-vertex degree of agraph. Discussiones Mathematicae Graph Theory, 38(3), 673–686.
[9] Munir, M., Nazeer, W., Kang, S. M., & Farooq, R. (2020). On ve-degree topological indices of graphs. Symmetry, 12(2), 321.
[10] Gutman, I., & Furtula, B. (2016). Degree-based topological indices. Springer, Cham.
[11] Liu, J., Wu, T., & Zhang, Y. (2021). Applications of degree-based indices in QSAR and QSPR studies. MATCH Communications in Mathematical and in Computer Chemistry, 86,5–28.
[12] Sharma, R., Gupta, S., & Kumar, A. (2022). Polynomial and hyper-polynomial ve-degree indices of graphs. Applied Mathematics and Computation, 421, 126964.
[13] Ahmad, M., Khan, Z., & Ali, R. (2023). Structural properties of cyclodextrin networks using ev-degree indices. MATCH Communications in Mathematical and in Computer Chemistry,90, 457–474.
[14] Singh, V., & Kumar, S. (2021). Computational approaches for topological indices using Maple. International Journal of Computer Mathematics, 98(12), 2356–2374