Abstract
The measure or determination of uncertainty of a system is known as entropy. After the rich idea of entropy, it gains attraction and interest in graph theory, due to its applications in applied mathematical chemistry. First time the idea graph entropy was used in 1955, to know the structural information of chemical networks or graphs. In mathematical chemistry, structures are the build-up of atoms/vertices and bonds/edges. Carbon nanotubes are also very famous since they have been used for memory devices and tissue engineering. This productive chemical structure is studied in this paper by inserting a cap on one and both ends. We measure the entropy of these three topologies of carbon nanotube. Some comparative work is also given, along with the analytical study of entropy measures of armchair carbon nanotubes.
Highlights
The entropy of a probability distribution known as a measure of the unpredictability of information content or a measure of the uncertainty of a system
FOR THE UNCAPPED CARBON NANOTUBE ACNT (β, γ ) Armchair carbon nanotube ACNT (β, γ ), with two types of vertices according to degree defined in Table 1 and edge types defined in Table 2, and p1, q1, are the order and size of ACNT (β, γ ), respectively
Proof: As we know that atom bond connectivity index is defined in the Table 3 by using the edge type of ACNT (β, γ ) which is defined in the Table 2
Summary
The entropy of a probability distribution known as a measure of the unpredictability of information content or a measure of the uncertainty of a system. Zuo et al.: Edge Weight Based Entropy of Different Topologies of Carbon Nanotubes advance stage due to the blessings of carbon nanotubes [16] These biological sensors are used to know the DNA and proteins from the body [17]. This article’s main contribution is to expand the number of applications and investigate various edge weightbased entropies of armchair carbon nanotubes, ACNT (β, γ ) , armchair carbon semi-capped nanotube, ACSCNT (β, γ ) and armchair carbon capped nanotube, ACCNT (β, γ ) We analyze these entropies and compare all three described structures by taking examples which are shown in Table 9 to Table 12 in further section, and depicted the results in Figure 5 to Figure 8. For more detail of this topology of armchair carbon nanotube and its variant are available in [45]
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