Further study of eccentricity based indices for benzenoid hourglass network

Hifza Iqbal; Muhammad Haroon Aftab; Ali Akgul; Zeeshan Saleem Mufti; Iram Yaqoob; Mustafa Bayram; Muhammad Bilal Riaz

doi:10.1016/j.heliyon.2023.e16956

Further study of eccentricity based indices for benzenoid hourglass network

Heliyon. 2023 Jun 7;9(6):e16956. doi: 10.1016/j.heliyon.2023.e16956. eCollection 2023 Jun.

Authors

Hifza Iqbal¹, Muhammad Haroon Aftab¹, Ali Akgul^{2

3

4}, Zeeshan Saleem Mufti¹, Iram Yaqoob¹, Mustafa Bayram⁵, Muhammad Bilal Riaz^{6

7

8}

Affiliations

¹ Department of Mathematics and Statistics, The University of Lahore, Lahore, 54500, Pakistan.
² Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.
³ Siirt University, Art and Science Faculty, Department of Mathematics, 56100, Siirt, Turkey.
⁴ Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia, Mersin, 10, Turkey.
⁵ Department of Computer Engineering, Biruni University, 34010, Topkapı, Istanbul, Turkey.
⁶ Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Poland.
⁷ Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon.
⁸ Department of Mathematics, University of Management and Technology, Pakistan.

Abstract

Topological Indices are the mathematical estimate related to atomic graph that corresponds biological structure with several real properties and chemical activities. These indices are invariant of graph under graph isomorphism. If top( $h_{1}$ ) and top( $h_{2}$ ) denotes topological index $h_{1}$ and $h_{2}$ respectively then $h_{1}$ approximately equal $h_{2}$ which implies that top( $h_{1}$ ) = top( $h_{2}$ ). In biochemistry, chemical science, nano-medicine, biotechnology and many other science's distance based and eccentricity-connectivity(EC) based topological invariants of a network are beneficial in the study of structure-property relationships and structure-activity relationships. These indices help the chemist and pharmacist to overcome the shortage of laboratory and equipment. In this paper we calculate the formulas of eccentricity-connectivity descriptor(ECD) and their related polynomials, total eccentricity-connectivity(TEC) polynomial, augmented eccentricity-connectivity(AEC) descriptor and further the modified eccentricity-connectivity(MEC) descriptor with their related polynomials for hourglass benzenoid network.

Keywords: Biological graph; Hourglass; Mathematics subject classification: 05C92; Naphthalene; Polynomial; Structure-activity; Structure-property.