International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2002 / Article

Open Access

Volume 31 |Article ID 206280 | https://doi.org/10.1155/S0161171202007925

Ancykutty Joseph, "On incidence algebras and directed graphs", International Journal of Mathematics and Mathematical Sciences, vol. 31, Article ID 206280, 5 pages, 2002. https://doi.org/10.1155/S0161171202007925

On incidence algebras and directed graphs

Received20 Jun 2001

Abstract

The incidence algebra I(X,) of a locally finite poset (X,) has been defined and studied by Spiegel and O'Donnell (1997). A poset (V,) has a directed graph (Gv,) representing it. Conversely, any directed graph G without any cycle, multiple edges, and loops is represented by a partially ordered set VG. So in this paper, we define an incidence algebra I(G,) for (G,) over , the ring of integers, by I(G,)={fi,fi*:V×V} where fi(u,v) denotes the number of directed paths of length i from u to v and fi*(u,v)=fi(u,v). When G is finite of order n, I(G,) is isomorphic to a subring of Mn(). Principal ideals Iv of (V,) induce the subdigraphs Iv which are the principal ideals v of (Gv,). They generate the ideals I(v,) of I(G,). These results are extended to the incidence algebra of the digraph representing a locally finite weak poset both bounded and unbounded.

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

 PDF Download Citation Citation
 Order printed copiesOrder
Views66
Downloads407
Citations

Related articles

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.