A Novel/Old Modification of the First Zagreb Index

Abstract

In the seminal paper [I. Gutman, N. Trinajstić, Chem. Phys. Lett. 1972, 17, 535–538], it was shown that total electron energy ((Formula presented.)) of any alternant hydrocarbon depends on the sum of the squares of the degrees of the corresponding molecular graph. Nowadays, this sum is known as the first Zagreb index. In the same paper, another molecular descriptor was proved to influence (Formula presented.), but that descriptor was never restudied explicitly. We call this descriptor as modified first Zagreb connection index and denote it by (Formula presented.). In this paper, chemical applicability of the molecular descriptor (Formula presented.) is tested for the octane isomers. Some basic properties of (Formula presented.) are also established here. Furthermore, the alkanes with maximum and minimum (Formula presented.) values are determined from the class of all alkanes having fixed number of carbon atoms.