Vukičević and Gašperov, in 2010, introduced a potentially useful topological index known as the Symmetric division deg (SDD) index. They showed that it best correlates when predicting the total surface area of polychlorobiphenyls (PCB). In agreement with the conclusions of Furtula et al. (Int J Quantum Chem 118(17):e25659, 2018), we have also discovered that the SDD index is potentially applicable due to its supremacy over other VDB molecular indices and high rate of correlation with the physicochemical properties of PCB. In this article, we analyze the relation between the SDD index and other physicochemical properties of PCBs, such as log water solubility, octanol-water partition ratio, with the aid of computers. We also compare it with other well-known vertex degree-based (VDB) indices. In this statistical fitting process, we also obtain the coefficient of determination <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42979_2025_3996_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">$r^2$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>r</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>, cross-validated squared correlation coefficient <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42979_2025_3996_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$q^2_{cv}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>q</mi> <mrow> <mi mathvariant="italic">cv</mi> </mrow> <mn>2</mn> </msubsup> </math></EquationSource> </InlineEquation>, the F test value for the standard error SE in the fit, and its corresponding test significance SF. We show that the SDD index has better correlation ability, with <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42979_2025_3996_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="82" /> </InlineMediaObject> <EquationSource Format="TEX">$r^2=0.9307$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>0.9307</mn> </mrow> </math></EquationSource> </InlineEquation> for log-water solubility and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42979_2025_3996_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="82" /> </InlineMediaObject> <EquationSource Format="TEX">$r^2=0.8615$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>0.8615</mn> </mrow> </math></EquationSource> </InlineEquation> for the octanol-water partition coefficient. Similarly, the cross-validated coefficient of determination values are <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42979_2025_3996_Article_IEq5.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">$q^2_{cv}=0.9285$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>q</mi> <mrow> <mi mathvariant="italic">cv</mi> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mn>0.9285</mn> </mrow> </math></EquationSource> </InlineEquation> for log-water solubility and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42979_2025_3996_Article_IEq6.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">$q^2_{cv}=0.8584$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>q</mi> <mrow> <mi mathvariant="italic">cv</mi> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mn>0.8584</mn> </mrow> </math></EquationSource> </InlineEquation> for the octanol-water partition coefficient. We also predicted the expected values for these two properties of PCBs whose experimental values are unavailable.

Comparative Analysis and Predictability of Physicochemical Properties of PCB Congeners Using Symmetric Division Degree Index on Molecular Graphs

期刊论文
发表日期：

2025年5月9日

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Lavanya Selvaganesh,
Abhay Rajpoot

摘要

Vukičević and Gašperov, in 2010, introduced a potentially useful topological index known as the Symmetric division deg (SDD) index. They showed that it best correlates when predicting the total surface area of polychlorobiphenyls (PCB). In agreement with the conclusions of Furtula et al. (Int J Quantum Chem 118(17):e25659, 2018), we have also discovered that the SDD index is potentially applicable due to its supremacy over other VDB molecular indices and high rate of correlation with the physicochemical properties of PCB. In this article, we analyze the relation between the SDD index and other physicochemical properties of PCBs, such as log water solubility, octanol-water partition ratio, with the aid of computers. We also compare it with other well-known vertex degree-based (VDB) indices. In this statistical fitting process, we also obtain the coefficient of determination $r^2$ $r^{2}$ , cross-validated squared correlation coefficient $q^2_{cv}$ $q_{cv}^{2}$ , the F test value for the standard error SE in the fit, and its corresponding test significance SF. We show that the SDD index has better correlation ability, with $r^2=0.9307$ $r^{2} = 0.9307$ for log-water solubility and $r^2=0.8615$ $r^{2} = 0.8615$ for the octanol-water partition coefficient. Similarly, the cross-validated coefficient of determination values are $q^2_{cv}=0.9285$ $q_{cv}^{2} = 0.9285$ for log-water solubility and $q^2_{cv}=0.8584$ $q_{cv}^{2} = 0.8584$ for the octanol-water partition coefficient. We also predicted the expected values for these two properties of PCBs whose experimental values are unavailable.