On ABC energy and its application to anticancer drugs

For a simple connected graph Γ with node set formula presented and degree sequence di, the atom-bond connectivity (ABC) matrix of Γ has an formula presented is adjacent to wj 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 Γ. 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.