International Journal of Mathematics And Computer Research

Abstract

This paper was designed to provide an introduction to the vector spaces used in graph theory. In graph theory, an area of mathematics, a cycle space is a vector space defined from an undirected graph; elements of the cycle space represent formal combinations of cycles in the graph. Cycle spaces allow one to use the
tools of linear algebra to study graphs. A cycle basis is a set of cycles that generates the cycle space. In the mathematical discipline of graph theory, the edge space and vertex space of an undirected graph are vector spaces defined in terms of the edge and vertex sets, respectively. These vector spaces make it possible to use techniques of linear algebra in studying the graph.