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

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

2012-02-08

arxiv.org/abs/1202.1817v1

Mathematics

Number Theory

Scientific paper

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.

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