Computing Analysis for First Zagreb Connection Index and Coindex of Resultant Graphs

A numeric parameter which studies the behaviour, structural, toxicological, experimental, and physicochemical properties of chemical compounds under several graphs’ isomorphism is known as topological index. In 2018, Ali and Trinajstić studied the first Zagreb connection index Z C 1 to evaluate the value of a molecule. This concept was first studied by Gutman and Trinajstić in 1972 to find the solution of π -electron energy of alternant hydrocarbons. In this paper, the first Zagreb connection index and coindex are obtained in the form of exact formulae and upper bounds for the resultant graphs in terms of different indices of their factor graphs, where the resultant graphs are obtained by the product-related operations on graphs such as tensor product, strong product, symmetric difference, and disjunction. At the end, an analysis of the obtained results for the first Zagreb connection index and coindex on the aforesaid resultant graphs is interpreted with the help of numerical values and graphical depictions.

Computing Analysis of Connection-Based Indices and Coindices for Product of Molecular Networks

Gutman and Trinajstić (1972) defined the connection-number based Zagreb indices, where connection number is degree of a vertex at distance two, in order to find the electron energy of alternant hydrocarbons. These indices remain symmetric for the isomorphic (molecular) networks. For the prediction of physicochemical and symmetrical properties of octane isomers, these indices are restudied in 2018. In this paper, first and second Zagreb connection coindices are defined and obtained in the form of upper bounds for the resultant networks in the terms of different indices of their factor networks, where resultant networks are obtained from two networks by the product-related operations, such as cartesian, corona, and lexicographic. For the molecular networks linear polynomial chain, carbon nanotube, alkane, cycloalkane, fence, and closed fence, first and second Zagreb connection coindices are computed in the consequence of the obtained results. An analysis of Zagreb connection indices and coindices on the aforesaid molecular networks is also included with the help of their numerical values and graphical presentations that shows the symmetric behaviour of these indices and coindices with in certain intervals of order and size of the under study (molecular) networks.

(Pyrrole-2,5-Diyl)-Bis(Nitronyl Nitroxide) and-Bis(Iminonitroxide): Specific Features of the Synthesis, Structure, and Magnetic Properties

In contrast to diradicals connected by alternant hydrocarbons, only a few studies have addressed diradicals connected by nonalternant hydrocarbons and their heteroatom derivatives. Here, the synthesis, structure, and magnetic properties of pyrrole-2,5-diyl–linked bis(nitronyl nitroxide) and bis(iminonitroxide) diradicals are described. The diradicals show characteristic electron spin resonance spectra in dilute glassy solutions, from which conclusions about the presence of distinct conformations, their symmetry, and interspin distance were made. X-ray diffraction analysis of the diradicals revealed that paramagnetic moieties lie in the plane of the pyrrole ring, because of the formation of an intramolecular hydrogen bond, ONO…H−N, with O…H distances of 2.15–2.23 Å. The N–O groups participating in the formation of H-bonds have greater bond lengths (~1.29 Å) as compared with nonparticipating groups (~1.27 Å). The nitronyl nitroxide and iminonitroxide diradicals showed an intramolecular antiferromagnetic interaction, with J = −77.3 and −22.2 cm−1, respectively (H = −2JS1⋅S2).

Anomalous effect of non-alternant hydrocarbons on carbocation and carbanion electronic configurations

Simple rules based on canonical structures allow for the prediction of a new class of triplet carbocation and carbanion species.