Yilmaz, FatihBozkurt, Durmus2020-03-262020-03-2620121110-757Xhttps://dx.doi.org/10.1155/2012/423163https://hdl.handle.net/20.500.12395/28471Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we consider one type of directed graph. Then we obtain a general form of the adjacency matrices of the graph. By using the well-known property which states the (i, j) entry of A(m) (A is adjacency matrix) is equal to the number of walks of length m from vertex i to vertex j, we show that elements of mth positive integer power of the adjacency matrix correspond to well-known Jacobsthal numbers. As a consequence, we give a Cassini-like formula for Jacobsthal numbers. We also give a matrix whose permanents are Jacobsthal numbers.en10.1155/2012/423163info:eu-repo/semantics/openAccessArticleQ3WOS:000307579300001Q2