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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.