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The Adjacency Matrix of One Type of Directed Graph and the Jacobsthal Numbers and Their Determinantal Representation.
- Source :
-
Journal of Applied Mathematics . 2012, p1-14. 14p. - Publication Year :
- 2012
-
Abstract
- 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 (i, j) entry of Am (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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 1110757X
- Database :
- Academic Search Index
- Journal :
- Journal of Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 84861749
- Full Text :
- https://doi.org/10.1155/2012/423163