Volume 25 • Issue 3 • PP: 312-321 • 2025
Computation of Weighted PI Index of Lexicographic product graphs and for Silicates Networks
View PDF Abstract
The study of chemical compounds’ molecular structures is one of the most cutting-edge uses of graph theory,
along with computer science, nanochemistry, network design in electrical and electronic engineering, and the
depiction of graphs in Google Maps. The degree and distance between vertices of a graph are the basis for
examining topological indices. The formula for computing the Weighted Padmakar Ivan index (WPI) of a
graph G is
PIw(G) = P e∈E(G)
[(dG(u) + dG(v)][|V (G)| − NG(e)].
Keywords
References
[1] I. Gutman, N. Trinajsti´c Graph theory and molecular orbitals: Total π-electron energy of alternate hydrocarbons, Chemical Physics Letters, vol. 17, no. 4, pp. 535–538, 1972.
[2] P. V. Khadikar, On a Novel Structural de-Scriptor pi, National Academy Science Letters, vol. 23, pp. 113–118, 2000.
[3] P. V. Khadikar, S. Karmarkar, Vijay K. Agrawal, A Novel PI Index and Its Applications to QSPR/QSAR Studies, Journal of Chemical Information and Computer Sciences, vol. 41, no. 4, pp. 934–949, 2001.
[4] A. R. Ashrafi, A. Loghman, PI index of zig-zag polyhex nanotubes, MATCH Commun. Math. Comput. Chem., vol. 55, no. 2, pp. 447–452, 2006.
[5] A. R. Ashrafi, A. Loghman, PI index of armchair polyhex nanotubes, Ars Combin, vol. 80, pp. 193–199, 2006.
[6] A. R. Ashrafi, F. Rezaei PI index of polyhex nanotori, MATCH Commun.Math. Comput. Chem, vol. 57, pp. 243–250, 2007.
[7] H. Deng, S. Chen, J. Zhang, The PI index of phenylenes, J. Math. Chem, vol. 41, no. 1, pp. 63–69, 2007.
[8] M. H. Khalifeh , H. Yousefi-Azari, A. R. Ashrafi Vertex and edge PI indices of Cartesian product graphs, Discrete Applied Mathematics, vol. 156, no. 10, pp. 1780–1789, 2008.
[9] Hammack R.,W. Imrich, S. Klavzar (2011) Handbook of product graphs: second edition, Discrete mathematics and its applications, CRC Press Taylor and Francis Group.
[10] L. You, R. Zhu, Z. You, The (Weighted) Vertex PI Index of Unicyclic Graphs, MATCH Communications in Mathematical and in Computer Chemistry, vol. 67, pp. 383–404, 2012.
[11] Ili´c A., Milosavljevi´c The weighted vertex PI index, Mathematical and Computer Modelling, vol. 57, no. 3, pp. 623–631, 2013.
[12] K. Pattabiraman, P. Kandan Weighted PI index of corona product of graphs, Discrete Mathematics, Algorithms and Applications, vol. 6, no. 4, pp. 1-9, 2014.
[13] L. Yan, J. Li, W. Gao, Weighted Vertex PI Index for Some Special Graphs, Scholars Journal of Engineering and Technology, vol. 3, no. 8, pp. 679–682, 2015.
[14] K. Pattabiraman, P. Kandan, OnWeighted PI Index of Graphs, Electronic Notes in Discrete Mathematics, vol. 53, pp. 225–238, 2016.
[15] Ma. G., Q. Bian, J. Wang, The weighted vertex PI index of bicyclic graphs, Discrete Applied Mathematics, vol. 247, pp. 309-321, 2018.
[16] C. Gopika, J. Geetha, K. Somasundaram , Weighted PI index of tensor product and strong product of graphs, Discrete Mathematics, Algorithms and Applications, vol. 13 no. 3, 2150019, 2021.
[17] R. Hemalatha, K. Somasundaram, Somber index of edge corona product of some classes of graphs, South East Asian J. of Mathematics and Mathematical Sciences, vol. 18, no. 3, pp. 307—316, 2022.
[18] T. P. Sandhiya, J. Geetha, K. Somasundaram, Total chromatic number for certain classes of lexicographic product graphs, Communications in Combinatorics and Optimization, vol. 9, no. 2, pp. 233–240, 2022.
[19] D. Prasantha Bharathi, T. Jayakumar, U.Bundit, R. Vadivel, P. Hammachukiattikul, C.Watcharaporn, On New Solutions of Fuzzy Hybrid Differential Equations by Novel Approaches, Journal of Mathematics, vol. 18, 7865973, 2023.
[20] K. Vishalakshi, S. Maragathavalli , D. Prasantha Bharathi, Carlos Martin-Barreiro, Xavier Cabezas , V´ıctor Leiva , Cecilia Castro, Addressing a decision problem through a bipolar Pythagorean fuzzy approach, A novel methodology applied to digital marketing: Heliyon, vol. 10, no. 3, e23991, 2023.
[21] L. Sushama, K. Sridhar, M. Roberts, (2023) Deep Learning-based Precision Diagnosis of Lung Diseases on the Internet of Medical Things (IoMT), C. R. Acad. Bulg. Sci. , vol. 76, no. 10, pp. 1536–1543, 2023.
[22] U. G. Muhammad, I. Mustafa, S. Faisal, C. Murat, H. Alphonse Computation of Zagreb Polynomial and Indices for Silicate Network and Silicate Chain Network, Journal of Mathematics, vol 9, 9722878, 2023.
[23] S. C. Manju, K. Swarnajyothi, J. Geetha, K. Somasundaram, On Vertex PI index of certain perfect graphs, lexicographic product of graphs, and some chemical networks, Journal of Intelligent & Fuzzy Systems, pp. 1–13, 2024.
Cite This Article
Choose your preferred format