%0 Journal Article
%T The Adjacency Matrix of One Type of Directed Graph and the Jacobsthal Numbers and Their Determinantal Representation
%A Fatih Y lmaz
%A Durmu  Bozkurt
%J Journal of Applied Mathematics
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/423163
%X Recently 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 (,) entry of  ( is adjacency matrix) is equal to the number of walks of length  from vertex  to vertex , we show that elements of th 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.
%U http://www.hindawi.com/journals/jam/2012/423163/