Recent research on nanostructures has demonstrated their importance and application in a variety of fields. Nanostructures are used directly or indirectly in drug delivery systems, medicine and pharmaceuticals, biological sensors, photodetectors, transistors, optical and electronic devices, and so on. The discovery of carbon nanotubes with Y-shaped junctions is motivated by the development of future advanced electronic devices. Because of their interaction with Y-junctions, electronic switches, amplifiers, and three-terminal transistors are of particular interest. Entropy is a concept that determines the uncertainty of a system or network. Entropy concepts are also used in biology, chemistry, and applied mathematics. Based on the requirements, entropy in the form of a graph can be classified into several types. In 1955, graph-based entropy was introduced. One of the types of entropy is edge-weighted entropy. We examined the abstract form of Y-shaped junctions in this study. Some edge-weight-based entropy formulas for the generic view of Y-shaped junctions were created, and some edge-weighted and topological index-based concepts for Y-shaped junctions were discussed in the present paper.

The future of multi-terminal networks and electronic appliances is made possible by nanotube junctions or branched nanotubes as building blocks. There are several different types of nanotube junctions used in nanoelectronics, such as junction electrical properties in L, T, Y, and Mei et al. [

We will discuss Y-type junctions of carbon nanotubes in this work. The name implies that Y-junctions have the shape of a Y-alphabet and are formed by joining three nanotubes. These three nanotubes are joined at a point known as the branching point, which is depicted in

Y-junctions may have additional sub-types depending on the topology of nanotubes. Single-walled nanotubes, for example, have three geometries: chiral, zig-zag, and armchair. So the created Y-junctions are known as the armchair carbon nanotube Y-junctions. Multi-walled nanotubes have all of these properties. The first nanotube was discovered in 1991 by Iijima [

The quantitative structure-property and activity relationships are solely concerned with predicting bio-activities and chemical or biological structure properties. In this method, topological indices and physicochemical properties are used to aid prediction. There is a substantial body of literature on topological descriptors of chemical structure that can be found in Ahmad et al. [

Topological descriptors which are very essential to compute our major results of entropy are given in the following definitions.

“The entropy of a probability distribution is known as a measure of the unpredictability of information content or a measure of the uncertainty of a system” by Shannon [

The literature on the concept is limited and sparse because it is new and has received little attention. This entropy was also studied on different types of nanotubes found by Imran et al. [

The main purpose of the research is to investigate some edge-weight-based entropy of Y-shaped junctions and their variants, as well as some comprehensive applications on the conceptual and applied approach of Y-shaped junctions and their variants. In the following section, we will investigate the structure of Y-shaped junctions and their variants using a basic formulation of edge-weight-based entropy for any simple, loop-less graph. In addition, we will present some key findings on the edge-weight-based entropy of Y-shaped junctions and their variants. Finally, we will come to a decision. There would be some interesting and significant literary references to intrigue readers to investigate Y-shaped junctions and their variants, edge-weight-based entropy, topological index, and entropy applications.

Manzoor et al. [

For the purposes of computation, the Y-junction structures are transformed into vertex-edge graphs, as described by Diudea et al. [

The Y-junctions examined in this research are constructed by the covalent connectivity of three armchair single-walled carbon nanotubes of given size, crossed at an angle of 120 degrees, and ascertained by the chiral vector

Let the parameter be integers. A Y-shaped junction graph is assembled by making an armchair which is called as branching point, and three carbon nanotubes of the same length of-layers of hexagons. It has number of vertices and the edges are in total. It has degree three vertices, and only degree 2 vertices. Each nanotube comprises faces of hexagons. While branching point comprise of faces. In these faces, hexagons, six heptagons and only three faces where nanotubes joined with branching point.

The notation is referred to as a graph of Y-shaped junction and it contained no vertex of one degree. The notation is an extension of graph of Y-shaped junction shown in the

The structure shown in the

Given below are some entropy measures for Y-junction and all its the variants.

Further some interesting topics and literature are given here for the readers attension. Some recent topological indices are discussed by Raza et al. [

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Entropy is a concept that determines the uncertainty of a system or network. Entropy concepts are also used in biology, chemistry, and applied mathematics. Based on the requirements, entropy in the form of a graph can be classified into several types. In 1955, graph-based entropy was introduced. One of the types of entropy is edge-weighted entropy. We examined the abstract form of Y-shaped junctions in this study. We created some edge-weight-based entropy formulas for the generic view of Y-shaped junctions. We discussed some edge-weighted and topological index-based concepts for Y-shaped junctions. Entropies of Y-junctions and their variants are studied for the first time in this study. We calculated the atom-bond-connectivity, Zagreb's first and second entropies for four different types of Y-shaped carbon nanotube junctions. Y-junctions and their structures are elaborated in numerical form using this method. The entire compound is described as a numeric digit. Instead of a complex structure, it will be easy to see as a number.