Quantifying some distance topological properties of the non-zero component graph

Fawaz E. Alsaadi; Faisal Ali; Imran Khalid; Masood Ur Rehman; Muhammad Salman; Madini Obad Alassafi; Jinde Cao; Fawaz E. Alsaadi; Faisal Ali; Imran Khalid; Masood Ur Rehman; Muhammad Salman; Madini Obad Alassafi; Jinde Cao

doi:10.3934/math.2021209

AIMS Mathematics

2021, Volume 6, Issue 4: 3512-3524. doi: 10.3934/math.2021209

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Quantifying some distance topological properties of the non-zero component graph

1.
Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
2.
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, 60800, Pakistan
3.
Department of Basic Sciences, Balochistan University of Engineering and Technology Khuzdar, Khuzdar, 89100, Pakistan
4.
Department of Mathematics, The Islamia University of Bahawalpur, 63100, Pakistan
5.
School of Mathematics, Southeast University, Nanjing 210096, P.R. China, and Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea

Received: 21 August 2020 Accepted: 15 January 2021 Published: 21 January 2021
MSC : 20E45, 05C25, 05C12, 05C07, 05C69, 15A27

Several bioactivities of chemical compounds in a molecular graph can be expected by using many topological descriptors. A topological descriptor is a numeric quantity which quantify the topology of a graph. By defining the metric on a graph related with a vector space, we consider this graph in the context of few topological descriptors, and quantify the Wiener index, hyper Wiener index, Reciprocal complimentary Wiener index, Schultz molecular topological index and Harary index. We also provide the graphical comparison of our results to describe the relationship and dependence of these descriptors on the involved parameters.
- distance,
- distance-based topological descriptors,
- non-zero component graph
Citation: Fawaz E. Alsaadi, Faisal Ali, Imran Khalid, Masood Ur Rehman, Muhammad Salman, Madini Obad Alassafi, Jinde Cao. Quantifying some distance topological properties of the non-zero component graph[J]. AIMS Mathematics, 2021, 6(4): 3512-3524. doi: 10.3934/math.2021209

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Abstract

Several bioactivities of chemical compounds in a molecular graph can be expected by using many topological descriptors. A topological descriptor is a numeric quantity which quantify the topology of a graph. By defining the metric on a graph related with a vector space, we consider this graph in the context of few topological descriptors, and quantify the Wiener index, hyper Wiener index, Reciprocal complimentary Wiener index, Schultz molecular topological index and Harary index. We also provide the graphical comparison of our results to describe the relationship and dependence of these descriptors on the involved parameters.

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