Nithya Sai Narayana


Farey Graph is associated with the sequence of irreducible fractions between 0 and 1  called the Farey Sequence and is constructed recursively by adding 2^{n-1} new vertices and 2^n  new edges at every  nth stage starting with K2. Farey Graphs are useful in representing the complex technical, social and biological networks of real world where the growth process depends upon the existing structure in iterative manner. The spanning trees of the graph indicate the connectivity of networks and random walks, dimer covering are some of the areas in which the enumeration of spanning trees are applied. In this paper the recurrence relation satisfied by Farey Graphs are studied and used to enumerate the number of spanning trees of Farey Graphs and some of related graphs. 
Keywords — Farey Graph, Recurrence relation, spanning trees

AMS Subject Classification: 05C05, 05C30, 05C85, 68R05

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