THE NEIGHBORHOOD HOMOLOGY CLASSIFICATION OF THE C4-FREE GRAPHS
无C_4图的邻域同调分类

A graph which does not contain a four-cycle is called the C4-free graph.Two graphs are called neighborhood homologous if their neighborhood homology groups areisomorphic. This paper proves that two connected C4-free graphs are neighborhood homologousif and only if they have identical bipartite characters and equal cyclomatic numbers.