Abstract: A formula for calculating the determinant and permanent of the adjacency matrix of a graph based on Sachs subgraphs on the graph was given, the author gave a vertex-deletion recursive formula for calculating the determinant and permanent of the adjacency matrix of the graph  respectively, and used  these recursive formulas to provide a method for calculating the determinant and permanent of the adjacency matrix of the color-ball graph  respectively. The results show that the determinant of the adjacency matrix of the color-ball graph is equal to the total differential of a function with 16 variables, and the permanent of the adjacency matrix of the color-ball graph is equal to the total differential of a function with 4 variables.

Key words: adxjacency matrix, determinant, permanent, color-ball graph, total differential