Geometric-arithmetic Index and Zagreb Indices of Certain Special Molecular Graphs

Abstract

In this paper, we determine the Geometric-arithmetic indexand Zagreb indicesof fan molecular graph, wheel molecular graph, gear fan molecular graph, gear wheel molecular graph, and their r-corona molecular graphs.

Second Atom-Bond Connectivity Index of Special Chemical Molecular Structures

“…Polyomino chain is one class of polyomino such that the connection of centres for adjacent squares constitutes a path 1 2 ⋅ ⋅ ⋅ , where is the centre of th square. Polyomino chain 4 is called a linear chain if the subgraph induced by all 3-degree vertices is a graph with − 2 squares. Furthermore, polyomino chain 4 is called a zigzag chain if the subgraph induced by all vertices with degree > 2 is path with − 1 edges.…”

“…There are several vertex distance-based and degree-based indices which are introduced to analyze the chemical properties of molecule graph, for instance, Wiener index, PI index, Szeged index, and atom-bond connectivity index. Several papers contributed to determining the indices of special molecular graphs (see Yan et al [1,2], Gao and Shi [3], Xi and Gao [4], and Dou et al [5] for more detail).…”

Degree Based Topological Indices of Zig Zag Chain

“…From this standpoint, the methods on topological index computation are very suitable and serviceable for developing countries in which they can yield the available biological and medical information of new drugs without chemical experiment hardware. Although there have been several contributions on distance-based indices and degreebased molecular structures, [10][11][12][13] the researches of topological index for certain special drug structures are still largely limited. Because of these, tremendous academic and industrial interest has been attracted to research the topological index of drug molecular structure from a mathematical point of view.…”

Degree-based indices computation for special chemical molecular structures using edge dividing method

“…It has been proved that topological indices reflect biochemical properties (such as the melting point, boiling point, toxicity and QSPR/QSAR study) of their corresponding compounds and drugs(see Wiener [1] and Katritzky et al, [2] for more details). Several articles contributed to determining the topological indices of special molecular graphs (See Yan et al [3] and [4], Gao and Shi [5] and [6], Gao and Wang [7], [8] and [9], Xi and Gao [10], Gao et al [11], Gao et al, [12] and [13], Gao and Farahani [14], Farahani and Gao [15], and Farahani [16], [17], [18], [19], [20], [21], [22], [23], [24] and [25] for more details). The notations and terminologies that were used but were undefined in this paper can be found in [26].…”