The forms of f2（n,k） and g2（n,k） were shown in Essentials ofCombinalorial Mathematics written by Mao Jingzhong. This paper gives the formsof f1（n,k） and g1 （n,k）, where 2.
In [3], a vector space associate with a graph G: 'its cycle space' was described over the two element field Z2. Here we generalize the theory to the ring Z to compute 1-dimensional homology group of a given 2-complex with a combination of algebraic and graph-theoretic method.
