The measure of irregularities of nanosheets

Abstract

Nanosheets are two-dimensional polymeric materials, which are among the most active areas of investigation of chemistry and physics. Many diverse physicochemical properties of compounds are closely related to their underlying molecular topological descriptors. Thus, topological indices are fascinating beginning points to any statistical approach for attaining quantitative structure–activity (QSAR) and quantitative structure–property (QSPR) relationship studies. Irregularity measures are generally used for quantitative characterization of the topological structure of non-regular graphs. In various applications and problems in material engineering and chemistry, it is valuable to be well-informed of the irregularity of a molecular structure. Furthermore, the estimation of the irregularity of graphs is helpful for not only QSAR/QSPR studies but also different physical and chemical properties, including boiling and melting points, enthalpy of vaporization, entropy, toxicity, and resistance. In this article, we compute the irregularity measures of graphene nanosheet, H-naphtalenic nanosheet, {\text{SiO}}_{2} nanosheet, and the nanosheet covered by {C}_{3} and {C}_{6}.

Resistance distance and sharp bounds of two-mode electrical networks

“…The topological index is a characteristic of graphs that remains unchanged under isomorphism, which is a property in graph theory [2][3][4][5][6]. These descriptors are distance, degree and eccentricity based, which help in understanding different networks such as biological, social networks and circuits in physics, and improve electrical circuits, identify critical components, study electrical flow and voltage distribution [7][8][9][10]. In chemistry, topological indices are useful in analysis of chemical reactions and enabling to predict molecular properties [11][12][13][14][15][16][17][18][19][20][21].…”

On Two-Stepwise Irregular Graphs

“…The irregularity index is a numerical value to evaluate the extent of irregularity in the whole graph. Several irregularity and topological indices were investigated for different types of graphs by several researchers [3,[17][18][19][20][21][22][23][24][25][26][27][28]. Albertson [29] proposed an irregularity index of a graph G as Irr(G) = uv∈E(G) |d(u) − d(v)|.…”

Computation of Mostar index for some graph operations

“…In the area of theoretical and computational chemistry, topological indices have become manifest to be significant descriptors since the activity of molecules relies on their structures, and the comparative ease with which these descriptors can be utilized in guessing the molecular properties resembled numerically intensive quantum chemical estimations [4–6]. A variety of topological descriptors is available for use, among which the most frequently applied in QSAR/QSPR researches for understanding the links between the potential physicochemical characteristics and the molecular structures are the vertex degree‐based topological indices [7–11] and the vertex‐distance based [12–16]. Thereby, the estimation of these numerical descriptors is one of the famous lines of research.…”