To clarify the space complexity of BFS traversal of a matrix:

When you start traversing a matrix from the corner, the maximum number of cells/nodes you can have in the queue is k where k is the number of cells on a diagonal line in the matrix, which means k = min(M, N).

When you start traversing a matrix from the centre, the maximum number of cells/nodes you can have in the queue is {1, 4, 8, 12, 16, ..., 4i} where i is the i-th layer. And such cells fit in a matrix of min size {1, 4, 9, 16, 25, ..., i*i} respectively. We know that i is min(M, N), so yet again we have space complexity of O(4 * min(M, N)) which is O(min(M,N)).

https://stackoverflow.com/a/75422161/9406517