Graph theory and molecular orbitals. XII. Acyclic polyenes

Abstract

A graph-theoretical study of acyclic polyenes is carried out with an emphasis on the influence of branching on several molecular properties. A definition of branching is given and several branching indices are analyzed. The case of polyenes without a Kekulé structure is discussed briefly. The main conclusions are: (a) thermodynamic stability of conjugated polyenes decreases with branching, but (b) reactivity, in general, increases with branching.

On the first Zagreb index and multiplicative Zagreb coindices of graphs

“…Among the oldest and most studied topological indices, there are two classical vertex-degree based topological indices-the first Zagreb index and second Zagreb index. These two indices first appeared in [14], and were elaborated in [15]. Later they were used in the structure-property model (see [20]).…”

On Use of the Variable Zagreb vM2 Index in QSPR: Boiling Points of Benzenoid Hydrocarbons

“…We considered χ, ε, WS, ws and ω indices because they have been used in the previous structure-boiling point studies of benzenoid hydrocarbons [13,14]. Below we give the best obtained models followed by the best models containing the The model (27) possesseses the lowest values of the standard errors of estimate, but the linear models based on the variable Zagreb M 2 index (10) and the variable connectivity index (18) are also very good models with the standard errors of estimate for the fit and cross-validated models of 6.8 (7. 2) o C and 8.0 (8.4) o C, respectively.…”

“…Originally, the Zagreb M 2 index together with the Zagreb M 1 index appeared in the topological formula for the total π-electron energy of conjugated molecules [17]: This index was first used as a branching index [18] and later as a useful molecular descriptor in various forms in QSPR and QSAR studies [19][20][21][22][23].…”

2D QSAR studies on a series of bifonazole derivatives with antifungal activity

“…In order to accomplish this task, a low dimensional classification rule (Fisher´s weight) was employed. As seen in Table 6, two descriptors are important for class discrimination, the Zagreb index by valence vertex degrees (ZM1V) that accounts for molecular branching in hydrogen-depleted structures 26 and the maximum negative intrinsic state difference in the molecules (MAXDN), which can be related to the nucleophilicity of the molecules. 27 The greater value of MAXDN suggests that it is the most appropriate descriptor to separate amine substituted compounds from nitro substituted ones.…”