Department
Mathematics
Document Type
Article
Publication Date
9-1-2014
Abstract
In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2) and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.
Journal Title
Electronic Journal of Graph Theory and Applications
Journal ISSN
2338-2287
Volume
2
Issue
2
First Page
129
Last Page
138
Digital Object Identifier (DOI)
10.5614/ejgta.2014.2.2.5