On the fibonacci numbers and F-polynomial of graphs

Abstract

The theory of graph polynomials and their applications in several branches of science was developed by many authors. Some of these polynomials are related to the matching polynomial. The Fibonacci polynomial, shortly F-polynomial, is also an analogy the matching polynomial. We show the basic properties and methods of calculation of the F-polynomial. Furthermore, the Fibonacci number of a graph, including its determination for certain types of graphs, is mentioned.