On irregularity descriptors of derived graphs

Wei Gao; Zahid Iqbal; Shehnaz Akhter; Muhammad Ishaq; Adnan Aslam; Wei Gao; Zahid Iqbal; Shehnaz Akhter; Muhammad Ishaq; Adnan Aslam

doi:10.3934/math.2020262

AIMS Mathematics

2020, Volume 5, Issue 5: 4085-4107. doi: 10.3934/math.2020262

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Research article

On irregularity descriptors of derived graphs

1.
School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China
2.
School of Natural Sciences, National University of Sciences and Technology, Islamabad 44000, Pakistan
3.
Department of Mathematics and Statistics, Institute of Southern Punjab, Multan 66000, Pakistan
4.
University of Engineering and Technology, Lahore (RCET) 54000, Pakistan

Received: 23 March 2020 Accepted: 20 April 2020 Published: 28 April 2020
MSC : 05C07, 05C09, 05C92

Topological indices are molecular structural descriptors which computationally and theoretically describe the natures of the underlying connectivity of nanomaterials and chemical compounds, and hence they provide quicker methods to examine their activities and properties. Irregularity indices are mainly used to characterize the topological structures of irregular graphs. Graph irregularity studies are useful not only for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies, but also for predicting their various physical and chemical properties, including toxicity, resistance, melting and boiling points, the enthalpy of evaporation and entropy. In this article, we establish the expressions for the irregularity indices named as the variance of vertex degrees, σ irregularity index, and the discrepancy index of subdivision graph, vertex-semi total graph, edge-semi total graph, total graph, line graph, paraline graph, double graph, strong double graph and extended double cover of a graph.
- irregularity indices,
- degree,
- total graph,
- double graph
Citation: Wei Gao, Zahid Iqbal, Shehnaz Akhter, Muhammad Ishaq, Adnan Aslam. On irregularity descriptors of derived graphs[J]. AIMS Mathematics, 2020, 5(5): 4085-4107. doi: 10.3934/math.2020262

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Abstract

Topological indices are molecular structural descriptors which computationally and theoretically describe the natures of the underlying connectivity of nanomaterials and chemical compounds, and hence they provide quicker methods to examine their activities and properties. Irregularity indices are mainly used to characterize the topological structures of irregular graphs. Graph irregularity studies are useful not only for quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies, but also for predicting their various physical and chemical properties, including toxicity, resistance, melting and boiling points, the enthalpy of evaporation and entropy. In this article, we establish the expressions for the irregularity indices named as the variance of vertex degrees, σ irregularity index, and the discrepancy index of subdivision graph, vertex-semi total graph, edge-semi total graph, total graph, line graph, paraline graph, double graph, strong double graph and extended double cover of a graph.

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