Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons

Degree-Based Topological Indices

“…14,15 However, initially these were intended to be used for a completely different purpose Figure 1. The molecular graph G of 2,4,4,6-tetramethylheptane with its vertex degrees indicated.…”

“…Analyzing the structure-dependency of total π-electron energy, 14 an approximate formula was obtained in which terms of the form…”

“…It was immediately recognized that these terms increase with the increasing extent of branching of the carbon-atom skeleton, 14,15 i.e., that these provide quantitative measures of molecular branching. Ten years later, in a review article, 42 Balaban et al included M 1 and M 2 among topological indices and named them "Zagreb group indices".…”

“…First, in the early 1980s, only a handful of topological indices were known, and the authors of the review 42 needed as many of them as possible. Second, in that time both authors of the paper 14 were members of the Theoretical Chemistry Group of the "Ruđer Bošković" Institute in Zagreb. Balaban et al probably wanted to avoid calling M 1 and M 2 by the name(s) of the discoverers, which otherwise is the usual practice (recall the Wiener, Hosoya, Balaban, Merrifield-Simmons, Narumi-Katayama indices, in addition to the Randić index).…”

The Values of Eccentricity-Based Topological Indices of Diamond Graphs

“…The first Zagreb index and second Zagreb index of graphs were defined by Gutman et al [12,13] . Then the first and second Zagreb eccentricity indices 1 ( ) and 2 ( ) were defined by Vukicevic et al [14].…”