# 34772

## Автор(ов):

4

Параметры публикации

## Тип публикации:

Статья в журнале/сборнике

## Название:

Cohomology of digraphs and (undirected) graphs

## Наименование источника:

• The Asian Journal of Mathematics

Vol. 19, № 5

• Boston

## Издательство:

• International Press

2015

## Страницы:

887-932
Аннотация
We construct a cohomology theory on a category of finite digraphs (directed graphs), which is based on the universal calculus on the algebra of functions on the vertices of the digraph. We develop necessary algebraic technique and apply it for investigation of functorial properties of this theory. We introduce categories of digraphs and (undirected) graphs, and using natural isomorphism between the introduced category of graphs and the full subcategory of symmetric digraphs we transfer our cohomology theory to the category of graphs. Then we prove homotopy invariance of the introduced cohomology theory for undirected graphs. Thus we answer the question of Babson, Barcelo, Longueville, and Laubenbacher about existence of homotopy invariant homology theory for graphs.

## Библиографическая ссылка:

Григорьян А.А., Lin Y.?., Muranov Y.?., Yau S.-T.?. Cohomology of digraphs and (undirected) graphs // The Asian Journal of Mathematics. 2015. Vol. 19, № 5. С. 887-932.