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The Adjacency Matrix of One Type of Directed Graph and the Jacobsthal Numbers and Their Determinantal Representation
- Source :
- J. Appl. Math., Journal of Applied Mathematics, Vol 2012 (2012)
- Publication Year :
- 2012
- Publisher :
- Hindawi Limited, 2012.
-
Abstract
- WOS: 000307579300001<br />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 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.<br />Selcuk UniversitySelcuk University<br />This research is supported by Selcuk University Research Project Coordinatorship (BAP).
Details
- ISSN :
- 16870042 and 1110757X
- Volume :
- 2012
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Mathematics
- Accession number :
- edsair.doi.dedup.....b0f8708d8ffb3fd70134f1a4a7911eb7