# Generation vs expansion BFS

I can not understand the difference between generation and expansion of nodes. How the time and space complexity of BFS are different in each two scenarios?

    Test at generation: 1+b+b2+...+b^d=O(b^d)

Test at expansion: 1+b+b2+...+b^d+(b^d−1)b=O(b^d+1)

• Could you please describe the algorithms for so-called "generation" and "expansion"? – xskxzr Jun 3 '18 at 13:43