Bond Additive Modeling 5. Mathematical Properties of the Variable Sum Exdeg Index

Abstract

Abstract. Recently, discrete and variable Adriatic indices have been introduced and it has been shown that the sum α -exdeg index is good predictor (when variable parameter is equal to 0.37 ) of the octanol-water partition coefficient for octane isomers. Here, we study mathematical properties of this descriptor. Namely, we analyze extremal graphs of this descriptor in the following classes: the class of all connected graphs, the class of all trees, the class of all unicyclic graphs, the class of all chemical graphs, the class of all chemical trees, the class of all chemical unicyclic graphs, the class of all graphs with given maximal degree, the class of all graphs with given minimal degree, the class of all trees with given number of pendant vertices, and the class of all connected graphs with given number of pendant vertices. Also, many open problems about variable Adriatic indices are proposed.

Degree-Based Topological Indices

“…This idea was pursued by Damir Vukičević, who elaborated an entire theory, [163][164][165][166] and many others. The chemical applicability of some selected Adriatic indices was examined.…”

On the zeroth-order general Randić index, variable sum exdeg index and trees having vertices with prescribed degree

“…Thereby, in order to make the extremal problem well defined we always take 3 ≤ n 1 ≤ n − 2. The trees with extremum SEI a values from the collection PT n,n 1 have already been determined in [28] for a > 1. Thereby, in this section, we solve this problem concerning SEI a for 0 < a < 1, which gives a partial solution of a problem posed in [28].…”

“…The topological index SEI a is very well correlated with octanol-water partition coefficient of octane isomers [27]. Detail about the chemical applicability and mathematical properties of this index can be found in the references [2,9,27,28,30]. A vertex having degree 1 is called pendent vertex and a vertex which have degree greater than 2 is named as branching vertex.…”

Inverse Sum Indeg Energy of Graphs

“…The spectrum of G, denoted by spec A (G), is the set of A-eigenvalues of G together with their multiplicities. The inverse sum indeg, (henceforth ISI) index, was studied in [24]. The ISI index is defined as…”