Topological indices are numerical descriptors that encode the structural information of molecular compounds using graph-theoretical representations in chemical graph theory. These indices are employed in the establishment of quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR) that serve to quantify various aspects of molecular topology. The M-polynomial provides an efficient and unified framework for handling complex computations and deriving a wide range of degree-based topological indices. Graph entropy measures are commonly applied to assess the structural complexity, randomness and information content of a graph. This article investigates the elliptic Sombor (ESO), reduced elliptic (RE) and modified reduced elliptic (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$^{m} \textit{RE}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mi>m</mi> </mmultiscripts> <mi mathvariant="italic">RE</mi> </mrow> </math></EquationSource> </InlineEquation>) indices for silicon carbide networks such as <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$SiC_{3} \textit{-I}[p,q]$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>i</mi> <msub> <mi>C</mi> <mn>3</mn> </msub> <mo>-</mo> <mi mathvariant="italic">I</mi> <mrow> <mo stretchy="false">[</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo stretchy="false">]</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$SiC_{3} \textit{-II}[p,q]$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>i</mi> <msub> <mi>C</mi> <mn>3</mn> </msub> <mo>-</mo> <mi mathvariant="italic">II</mi> <mrow> <mo stretchy="false">[</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo stretchy="false">]</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$SiC_{3} \textit{-III}[p,q]$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>i</mi> <msub> <mi>C</mi> <mn>3</mn> </msub> <mo>-</mo> <mi mathvariant="italic">III</mi> <mrow> <mo stretchy="false">[</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo stretchy="false">]</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> by computing their corresponding M-polynomials. Next, we introduce entropy measures based on the elliptic Sombor (ESO), reduced elliptic (RE) and modified reduced elliptic (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$^{m} \textit{RE}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mi>m</mi> </mmultiscripts> <mi mathvariant="italic">RE</mi> </mrow> </math></EquationSource> </InlineEquation>) indices and derive their corresponding expressions for the aforementioned networks. Furthermore, the behavior of the elliptic Sombor (ESO), reduced elliptic (RE) and modified reduced elliptic (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">$^{m} \textit{RE}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mi>m</mi> </mmultiscripts> <mi mathvariant="italic">RE</mi> </mrow> </math></EquationSource> </InlineEquation>) indices, along with their associated entropy measures, is analyzed through both graphical visualization and numerical computation. Furthermore, cubic regression models are employed in the QSPR analysis to establish a strong correlation between elliptic-type entropy measures and the cohesive energy of the investigated silicon carbide networks. Subsequently, curve fitting is employed to explore the relationship between the elliptic-type indices and the corresponding entropy measures. These indices and entropy measures serve as valuable tools for predicting physicochemical properties and providing deeper insight into the structural characteristics of the analyzed silicon carbide networks.

QSPR Analysis of Elliptic-type Entropy Measures and Their Correlation with Elliptic-type Indices of Silicon Carbide Networks

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发表日期：

2026年2月9日

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Jayjit Barman,
Shibsankar Das

摘要

Topological indices are numerical descriptors that encode the structural information of molecular compounds using graph-theoretical representations in chemical graph theory. These indices are employed in the establishment of quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR) that serve to quantify various aspects of molecular topology. The M-polynomial provides an efficient and unified framework for handling complex computations and deriving a wide range of degree-based topological indices. Graph entropy measures are commonly applied to assess the structural complexity, randomness and information content of a graph. This article investigates the elliptic Sombor (ESO), reduced elliptic (RE) and modified reduced elliptic ( $^{m} \textit{RE}$ $^{m} RE$ ) indices for silicon carbide networks such as $SiC_{3} \textit{-I}[p,q]$ $S i C_{3} - I [p, q]$ , $SiC_{3} \textit{-II}[p,q]$ $S i C_{3} - II [p, q]$ and $SiC_{3} \textit{-III}[p,q]$ $S i C_{3} - III [p, q]$ by computing their corresponding M-polynomials. Next, we introduce entropy measures based on the elliptic Sombor (ESO), reduced elliptic (RE) and modified reduced elliptic ( $^{m} \textit{RE}$ $^{m} RE$ ) indices and derive their corresponding expressions for the aforementioned networks. Furthermore, the behavior of the elliptic Sombor (ESO), reduced elliptic (RE) and modified reduced elliptic ( $^{m} \textit{RE}$ $^{m} RE$ ) indices, along with their associated entropy measures, is analyzed through both graphical visualization and numerical computation. Furthermore, cubic regression models are employed in the QSPR analysis to establish a strong correlation between elliptic-type entropy measures and the cohesive energy of the investigated silicon carbide networks. Subsequently, curve fitting is employed to explore the relationship between the elliptic-type indices and the corresponding entropy measures. These indices and entropy measures serve as valuable tools for predicting physicochemical properties and providing deeper insight into the structural characteristics of the analyzed silicon carbide networks.