Some results of graph homotopy theory.

Two spaces are said to be homotopy equivalent in classical homotopy theory if one space may be continuously deformed into the other. However, this theory disregards the discrete nature of graphs. Because of this, there is a discrete homotopy theory that distinguishes between a graph's vertices and edges. It's called A-homotopy theory, the purpose of this paper is to provide and investigate a novel notion of graph homotopy with an equivalence definition. The 3-cycle 퐶3 and 4-cycle 퐶4 are conteactible, that is, they are viewed as being identical to a single vertex. We define equivalence graph Homotopy proposing an alternate definition. [ABSTRACT FROM AUTHOR]