In the seminal paper [I. Gutman, N. Trinajstić, Chem. Phys. Lett. 1972, 17, 535-538], it was shown that total electron energy (Eπ ) 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 Eπ , but that descriptor was never restudied explicitly. We call this descriptor as modified first Zagreb connection index and denote it by ZC1* . In this paper, chemical applicability of the molecular descriptor ZC1* is tested for the octane isomers. Some basic properties of ZC1* are also established here. Furthermore, the alkanes with maximum and minimum ZC1* values are determined from the class of all alkanes having fixed number of carbon atoms.
In this work, the novel iterative transformation technique and homotopy perturbation transformation technique are used to calculate the fractional-order gas dynamics equation. In this technique, the novel iteration method and homotopy perturbation method are combined with the Elzaki transformation. The current methods are implemented with four examples to show the efficacy and validation of the techniques. The approximate solutions obtained by the given techniques show that the methods are accurate and easy to apply to other linear and nonlinear problems.
Abstract. This work is devoted to establish a general expression for calculating the bond incident degree (BID) indices of polyomino chains and to characterize the extremal polyomino chains with respect to several well known BID indices.
The modified first Zagreb connection index (ZC Ã 1 ) is a molecular descriptor, which was initially appeared within a formula of the total electron energy of alternant hydrocarbons in 1972. In a recent paper [A. Ali, N. Trinajstić, A novel/old modification of the first Zagreb index, Mol. Inform. 37 (2018) 1800008], it was observed that the molecular descriptor ZC Ã 1 correlates well with the entropy and acentric factor of octane isomers. In this article, the molecules with the first three maximal ZC Ã 1 values as well as the first three minimal ZC Ã 1 values are determined from the family of all alkanes with n carbon atoms, for n ! 6. This extends the main results of the aforementioned paper.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.