Permutation of any two rows or columns in an incidence matrix simply corresponds to relabelling the vertices and edges of the same graph. Conversely, two graphs X and Y are isomorphic if and only if their incidence matrices A(X) and A(Y) differ only by permutations of rows and columns.
Can someone explain me what does it mean, with an example. What exactly does "permutation of any two rows or columns" over hear means?
"Permutation" here means "exchange". Consider the following node-node incidence matrix:
It defines a graph with vertices 0, 1, 2 where the edges constitue a circle 0-1-2-0. If the first two rows are exchanged, we obtain
where the circle is 0-2-1-0. This graph is obtained from the initial graph by relabelling 1 to 2 and vice versa. This means that both graphs are "identical up to renaming of vertices", i.e. they are isomorphic.