In a graph $G=(V,E)$, the temperature $T_x$ of a vertex $x\in V$ is defined as $T_x=d_x/n-d_x$, where n is the order of G and $d_x$ is the valency/degree of x. A topological/graphical index $\mathrm{\text{GI}}$ is a map $\mathrm{\text{GI}}:\sum \to ℝ$, where ∑ (respectively, $ℝ$) is the set of simple connected graphs (respectively, real numbers). Graphical indices are employed in quantitative structure-property relationship (QSPR) modeling to predict physicochemical/thermodynamic/biological characteristics of a compound. A temperature-based graphical index of a chemical graph G is defined as ${\mathrm{\text{GI}}}_T:={\sum }_{\mathrm{\text{edges}}}f(T_x,T_y)$, where $f(T_x,T_y)$ is a symmetric 2-variable map. In this paper, we introduce two new novel temperature-based indices named as the reduced reciprocal product-connectivity temperature ($\mathrm{\text{RRPT}}$) index and the geometric-arithmetic temperature ($\mathrm{\text{GAT}}$) index. The predictive potential of these indices has been investigated by employing them in structure-property modeling of the total $\pi$-electronic energy $E_{\pi }(\beta )$ of benzenoid hydrocarbons. In order to validate the statistical inference, the lower 30 BHs have been opted as test molecules as their experimental data for $E_{\pi }(\beta )$ is also publicly available. First, we employ a computer-based computational method to compute temperature indices of 30 lower BHs. Certain QPSR models are proposed by utilizing the experimental data of $E_{\pi }$ for the BHs. Our statistical analysis suggests that the most efficient regression models are, in fact, linear. Our statistical analysis asserts that both $\mathrm{\text{RRPT}}$ and $\mathrm{\text{GAT}}$ outperformed all the existing temperature indices for correlating $E_{\pi }$ for the BHs. The results suggest their further employability in QSPR modeling. Importantly, our research contributes toward countering proliferation of graphical indices.

在图表中$G=（V,乙）$， 气温${\mathrm{时间}}_X$一个顶点的$X\epsilon V$定义为${\mathrm{时间}}_X=d_X/n-d_X$，其中n是G的阶数，$d_X$是x的化合价/度数。拓扑/图形索引$\mathrm{\text{胃肠道}}$是一张地图$\mathrm{\text{胃肠道}}:\Sigma \to ℝ$，其中 Σ （分别为$ℝ$）是简单连通图（分别为实数）的集合。图形索引用于定量结构-性质关系 (QSPR) 建模，以预测化合物的物理化学/热力学/生物学特性。化学图G的基于温度的图指数定义为${\mathrm{\text{胃肠道}}}_{\mathrm{时间}}:={\Sigma }_{\mathrm{\text{边缘}}}F（{\mathrm{时间}}_X,{\mathrm{时间}}_y）$， 在哪里$F（{\mathrm{时间}}_X,{\mathrm{时间}}_y）$是对称的 2 变量映射。在本文中，我们引入了两种新的基于温度的指数，称为减少的倒数产品连接温度（$\mathrm{\text{RRPT}}$）指数和几何算术温度（$\mathrm{\text{盖特}}$） 指数。通过将这些指数用于总结构-性质建模，研究了它们的预测潜力。$\pi$-电子能源${乙}_{\pi }（\beta ）$苯系烃。为了验证统计推论，选择较低的30个BH作为测试分子作为其实验数据${乙}_{\pi }（\beta ）$也是公开的。首先，我们采用基于计算机的计算方法来计算 30 个较低 BH 的温度指数。利用以下实验数据提出了某些 QPSR 模型${乙}_{\pi }$对于 BH。我们的统计分析表明，最有效的回归模型实际上是线性的。我们的统计分析表明，两者$\mathrm{\text{RRPT}}$和$\mathrm{\text{盖特}}$优于所有现有的相关温度指数${乙}_{\pi }$对于 BH。结果表明它们在 QSPR 建模中具有进一步的可应用性。重要的是，我们的研究有助于遏制图形索引的扩散。