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Tutte polynomial for a small world connected copies of Farey graphs |
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PP: 767-774 |
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doi:10.18576/amis/180409
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Author(s) |
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A. Elsaid,
A. A. El-Atik,
Fatma El-Safty,
A. W. Aboutahoun,
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Abstract |
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| The Tutte polynomial has an essential rule in several applications such as networks and many areas of science, for example,
combinatorics, biology, and statistical mechanics. In this paper, we investigate a two-variable polynomial graph invariant of the Tutte
polynomial of a graph. Using the two new models, an established form of the Farey graph is given, and a modification of the basic
theory for these two new models is introduced. The Tutte polynomial is used to determine the number of spanning trees, as well as
the number of connected spanning subgraphs. A deduction of the exact expressions for the chromatic polynomial and the reliability
polynomial of graphs are presented. Moreover, we apply our models to establish the form of the Koch curve. |
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