characterize all connected graph which the rank of its adjacency matrix is 2.
I know that when a graph is connected,the power of adjacency matrix has no zero entry.
it seems that won't help!
I really don't know what to do!I need a point to start,thank you very much!
The rank of matrix is 2 means that every three rows are linear dependend. You need to take two linear independent rows (and understand what it means if you can't do it). Then you need to understand that since we are in the ring of 0 and 1 (only possible values for numbers in matrix) there is really few linear combinations for this two rows. And every other row is one if them. Then you solve the problem.