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,...) 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

Another proof of Pell identities by using the determinant of tridiagonal matrix

In this paper, another proof of Pell identities is presented by using the determinant of tridiagonal matrices. It is calculated via the Laplace expansion