Inverse Sum Indeg Index (Energy) with Applications to Anticancer Drugs

For a simple graph with vertex set $\{v_1,v_2,\dots ,v_n\}$ with degree sequence $d_{v_i}$ of vertex $v_i,i=1,2,\dots ,n$, the inverse sum indeg matrix ($ISI$-matrix) $A_{ISI}\left(G\right)={\left(a_{ij}\right)}_{n\times n}$ of G is defined by $a_{ij}=\frac{d_{v_i}{d}_{v_j}}{d_{v_i}+d_{v_j}},$ if $v_i$ is adjacent to $v_j$, and zero, otherwise. The multiset of eigenvalues of $A_{ISI}\left(G\right)$ is the $ISI$-spectrum of G and the sum of their absolute values is the $ISI$-energy of $G$. In this paper, we modify the two results of (Li, Ye and Broersma, 2022), give the correct characterization of the extremal graphs and thereby obtain better bounds than the already known results. Moreover, we also discuss the QSPR analysis and carry the statistical modelling (linear, logarithmic and quadratic) of the physicochemical properties of anticancer drugs with the $ISI$-index (energy).