Ahmet A. Husainov, Hamza Çalişici, “Flows in graphs and the homology of free categories”, Algebra Discrete Math., 2003, Issue 2,Pages <nobr>36

RESEARCH ARTICLE

Flows in graphs and the homology of free categories

Ahmet A. Husainov^a, Hamza Çalişici^b

^a Department of Computer Technologies, Komsomolsk-on-Amur State Technical University, prosp. Lenina, 27, Komsomolsk-on-Amur, 681013, Russia
^b Amasya Egitim Fakultesi, Matematik Bolumu, Ondokuz Mayis University, Amasya, 05189, Turkey

Abstract: We study the $R$-module of generalized flows in a graph with coefficients in the $R$-representation of the graph over a ring $R$ with 1 and show that this $R$-module is isomorphic to the first derived functor of the colimit. We generalize Kirchhoff's laws and build an exact sequence for calculating the $R$-module of flows in the union of graphs.

Keywords: homology of categories, derived of colimit, flows in graphs, Kirchhoff laws.

MSC: 18G10, 68R10

Received: 13.05.2003
Revised: 25.06.2003

Language: English