Séminaire Lotharingien de Combinatoire, B18s (1987), 8 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1988, 358/S-18, p.
127-134.]
Ulrich Oberst
(Co)-homologie von Graphen and Invarianten
Abstract.
This article emeged from a two-hour lecture on graph theory for
students with standard knowledge of algebra. It is known since
Poincaré (keyword: Analysis situs) that graph theory can be
conceived as 1- or at most 2-dimensional special case of combinatorial
(today: algebraic) topology. Viewed in this way, the method of my
lecture was the use of elementary homological algebra and of arbitrary
coefficient groups in (co-)homology. I introduce - to my knowledge -
new homological invariants of a graph, namely the invariant
factors of the finite group
Z{edges of G}/(B1(G)+H1(G)),
and I derive some of their properties.
Furthermore, I demonstrate the method of this lecture with the
contraction and the Meyer-Vietoris sequence.
The following version is available:
The paper has been finally published under the title
"Some combinatorial properties of the Thue-Morse sequence
and a problem in semigroups" in
Theoret. Comput. Sci. 63 (1989), 333-348.