Abstract
Entropy in general, is termed as the measure or determination of the improbability of a system. This opulent idea has invited wide interest while discussing and dealing with the multidimensional aspects of applied mathematical chemistry. This idea, pertaining to graph theory, was first applied in 1955. In the same way as nodes and edges create a graph of a network or system in mathematical chemistry, networks are built up in nodes and edges to form a graph of a network or system. Carbon nanotubes, on the other hand, are well-known for their application in memory devices as well as tissue engineering. This useful chemical structure, a carbon nanotube with one-end and both-end caps, is investigated. The entropy of these three carbon nanotube topologies is measured. Beside the analytical investigation of entropy measure of armchair carbon nanotubes, some comparison work is presented.
Highlights
The notion ACN T (β, γ), is for an armchair carbon nanotube, it has two types of vertices according to degree defined in Table 1 and edge types defined in Table 2, and p1 are the order and q1, size of ACN T (β, γ)
Authors of [42], determined the topological indices based on the degree of armchair carbon nanotube ACN T (β, γ)
For three cases of armchair carbon nanotubes, we calculated entropy based on edge weight, namely armchair car
Summary
The notion ACSCN T (β, γ) , is for the armchair carbon semi-capped nanotub, which has two different types of vertices, according to the fact established in Table 4, while edge distribution is defined in Table 5, given p2, q2, are the order and size of ACSCN T (β, γ) , respectively. Theorem 15: Let ΩReZG3 is the edge weight based redefined third Zagreb entropy for the graph G ∼= ACN T (β, γ) , ΩReZG3 (G) is ΩReZG3 (G) =. Theorem 16: Let ΩM1 is the edge weight based first Zagreb entropy for the graph G =∼= ACSCN T (β, γ) , ΩM1 (G) is mined in the Table 3. We will use the the value of redefined third Zagreb index, and resulted in TABLE 6: ACSCN T (β, γ) graph’s Topological Indices. Theorem 18: Let ΩHM is the edge weight based hyper Zagreb entropy for the graph G =∼= ACSCN T (β, γ) , log 416β × 550β × 654βγ−72β log (54βγ − 21β) −. Theorem 19: Let ΩAZI is the edge weight based augmented Zagreb entropy for the graph G =∼= ACSCN T (β, γ) , . We will use the the value of augmented Zagreb index in the Equation 12, and resulted in
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