The adjacency matrix of one type of graph and the Fibonacci numbers

Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we investigate relationships between one type of graph and well-known Fibonacci sequence. In this content, we consider the adjacency matrix of one type of graph with 2k (k=1,2,...

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Bibliographic Details
Published in:arXiv.org 2012-02
Main Authors: Yılmaz, Fatih, \c{S}erife Burcu Bozkurt, Bozkurt, Durmuş
Format: Article
Language:English
Subjects:
Apexes
Fibonacci numbers
Graph theory
Sequences
Online Access:Get full text
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Summary:Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we investigate relationships between one type of graph and well-known Fibonacci sequence. In this content, we consider the adjacency matrix of one type of graph with 2k (k=1,2,...) vertices. It is also known that for any positive integer r, the (i,j)th entry of A^{r} (A is the adjacency matrix of the graph) is just the number of walks from vertex i to vertex j, that use exactly k edges.
ISSN:2331-8422