×

Redefined Zagreb indices of rhombic, triangular, hourglass and jagged-rectangle benzenoid systems. (English) Zbl 1452.05035

Summary: In the fields of mathematical chemistry and chemical graph theory, a topological index generally called a connectivity index is a kind of a molecular descriptor that is calculated in perspective of the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which depict its topology and are graph invariant up to graph isomorphism. Topological indices are used for example in the progression of quantitative structure-activity relationships (QSARs) in which the common activity or distinctive properties of atoms are connected with their molecular structure. There are in excess of 140 topological indices but none of them totally describe the molecular compound completely so there is dependably a space to characterize and register new topological indices. Benzenoid Systems are utilized basically as an intermediate to make different synthetic compounds. In this report we aim to compute redefined Zagreb indices for Zigzag, Rhombic, triangular, Hourglass and Jagged-rectangle Benzenoid systems.

MSC:

05C09 Graphical indices (Wiener index, Zagreb index, Randić index, etc.)
05C10 Planar graphs; geometric and topological aspects of graph theory
05C12 Distance in graphs
05C15 Coloring of graphs and hypergraphs
05C22 Signed and weighted graphs
05C31 Graph polynomials
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] S. Ahmad, H. M. A. Siddiqui, A. Ali, M. R. Farahani, M. Imran, and I. N. Cangul, “On Wiener index and Wiener polarity index of some polyomino chains”, Journal of discrete mathematical sciences and cryptography, vol. 22, no. 7, pp. 1151-1164, 2019, doi: 10.1080/09720529.2019.1688965 · Zbl 1495.05035
[2] A. Ali , W. Nazeer, M. Munir, and S. M. Kang, “M-polynomials and topological indices of zigzag and rhombic Benzenoid systems”, Open chemistry, vol. 16, no. 1, pp. 73-78, Jan. 2018, doi: 10.1515/chem-2018-0010
[3] U. Ali, Y. Ahmad, and M. S. Sardar, “On 3-total edge product cordial labeling of tadpole, book and flower graphs”, Open journal of mathematical sciences, vol. 4, no. 1, pp. 48-55, 2020, doi: 10.30538/oms2020.0093
[4] F. Asif, Z. Zahid, and S. Zafar, “Leap Zagreb and leap hyper-Zagreb indices of Jahangir and Jahangir derived graphs”, Engineering and Applied Science Letter, vol. 3, no. 2, pp. 1-8, 2020. [On line]. Available: https://bit.ly/3dm05rH
[5] A. T. Balaban, I. Motoc, D. Bonchev, and O. Mekenyan, “Topological indices for structure-activity correlations”, in Steric effects in drug design, vol. 114, Berlin: Springer, 1983, pp. 21-55, doi: 10.1007/BFb0111212
[6] M. Cancan, S. Ediz, andM. R. Farahani , “On ve-degree atom-bond connectivity, sum-connectivity, geometric-arithmetic and harmonic indices of copper oxide”,Eurasian chemical communications, vol. 2, no. 5, pp. 641-645, 2020, doi: 10.33945/SAMI/ECC.2020.5.11
[7] B. Furtula, A. Graovac, and D. Vukičević, “Augmented zagreb index”, Journal of mathematical chemistry, vol. 48, no. 2, pp. 370-380, Aug. 2010, doi: 10.1007/s10910-010-9677-3 · Zbl 1196.92050
[8] W. Gao andM. R. Farahani , “The hyper-zagreb index for an infinite family of nanostar dendrimer”, Journal of discrete mathematical sciences and cryptography , vol. 20, no. 2, pp. 515-523, 2017, doi: 10.1080/09720529.2016.1220088 · Zbl 1495.05042
[9] W. Gao andM. R. Farahani , “The zagreb topological indices for a type of benzenoid systems jagged-rectangle”, Journal of interdisciplinary mathematics, vol. 20, no. 5, pp. 1341-1348, 2017, doi: 10.1080/09720502.2016.1232037
[10] W. Gao, L. Shi, andM. R. Farahani , “Szeged Related Indices of TUAC_6[p, q]”, Journal of discrete mathematical sciences and cryptography , vol. 20, no. 2, pp. 553-563, 2017, doi: 10.1080/09720529.2016.1228312 · Zbl 1511.92101
[11] W. Gao , M. Younas, A. Farooq, A. Virk, andW. Nazeer , “Some reverse degree-based topological indices and polynomials of dendrimers”, Mathematics, vol. 6, no. 10, p. 214, Oct. 2018, doi: 10.3390/math6100214
[12] I. Gutman, B. Rucić, N. Trinajstić, and C. F. Wilcox Jr. “Graph theory and molecular orbitals. XII. Acyclic polyenes”, The journal of chemical physics, vol. 62, no. 9, p. 3399, May 1975, doi: 10.1063/1.430994
[13] I. Gutman andN. Trinajstić , “Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons”, Chemical physics letters, vol. 17, no. 4, pp. 535-538, Dec. 1972, doi: 10.1016/0009-2614(72)85099-1
[14] Y. Huang, B. Liu and L. Gan, “Augmented zagreb index of connected graphs”, MATCH communication in mathematical and in computer chemistry, vol. 67, no. 2, pp. 483-494, 2012. [On line]. Available: https://bit.ly/2NdkHYe · Zbl 1289.05065
[15] Y. C. Kwun, A. Ali , W. Nazeer , M. A. Chaudhary, andS. M. Kang , “M-polynomials and degree-based topological indices of triangular, Hourglass, and Jagged-Rectangle Benzenoid systems”, Journal of chemistry, vol. 2018, Art ID. 8213950, Dec. 2018, doi: 10.1155/2018/8213950
[16] J.-B. Liu, M. Younas , M. Habib, M. Yousaf, andW. Nazeer , “M-polynomials and degree-based topological indices of VC_5C_7[p,q] and HC_5C_7[p,q] Nanotubes”, IEEE access, vol. 7, pp. 41125-41132, Mar. 2019, doi: 10.1109/ACCESS.2019.2907667
[17] M. Munir , W. Nazeer , S. Rafique, and S. Kang, “M-polynomial and degree-based topological Indices of polyhex nanotubes”, Symmetry, vol. 8, no. 12, p. 149, 2016, doi: 10.3390/sym8120149
[18] P. S. Ranjini, V. Lokesha, and A. Usha, “Relation between phenylene and hexagonal squeeze using harmonic index”, International journal of graph theory; vol. 1, pp. 116-121, 2013
[19] A. Shah and S. A. U. H. Bokhary, “On chromatic polynomial of certain families of dendrimer graphs”, Open journal of mathematical sciences , vol. 3, no. 1, pp. 404-416, 2019, doi: 10.30538/oms2019.0083
[20] A. Tabassum, M. A. Umar, M. Perveen, and A. Raheem, “Antimagicness of subdivided fans”, Open journal of mathematical sciences , vol. 4, no. 1, pp. 18-22, 2020, doi: 10.30538/oms2020.0089
[21] M. A. Umar , N. Ali, A. Tabassum , and B. R. Ali, “Book graphs are cycle antimagic”, Open journal of mathematical sciences , vol. 3, no. 1, pp. 184-190, 2019, doi: 10.30538/oms2019.0061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.