Abstract
A definition of a set of Fibonacci graphs is introduced which allows construction of several counting polynomials of very large graphs quite easily using a pencil-and-a-paper approach. These polynomials include matching, sextet, independence, Aihara and Hosoya polynomials. Certain combinatorial properties of Kekule counts of benzenoid hydrocarbons are given. A relation to a new topological function that counts the cardinality of graph topology [23] is given.
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