On $ABC$ energy and its application to anticancer drugs

For a simple connected graph $\mathrm{\Gamma }$ with node set $V(\mathrm{\Gamma })=\{w_1,w_2,\dots ,w_n\}$ and degree sequence $d_i$, the atom-bond connectivity ( $ABC$) matrix of $\mathrm{\Gamma }$ has an $(ij)$-th entry $\sqrt{\frac{d_i+d_j-2}{d_i{d}_j}}$ if $w_i$ is adjacent to $w_j$ and $0$, otherwise. The multiset of all eigenvalues of $ABC$ matrix is known as the $ABC$ spectrum and their absolute sum is known as the $ABC$ energy of $\mathrm{\Gamma }.$ Two graphs of same order are known as $ABC$ equienergetic if they have the same $ABC$ energy but share different $ABC$ spectrum. We describe the $ABC$ spectrum of some special graph operations and as an application, we construct the $ABC$ equienergetic graphs. Further, we give linear regression analysis of $ABC$ index/energy with the physical properties of anticancer drugs. We observe that they are better correlated with $ABC$-energy.