def rotate(path, j):
    """
    rotate list of vertices at vertex j
    :param path: a list of nodes
    :param j: vertex to perform rotation at
    :return: rotated path
    """
    if j in path:
        i = path.index(j)
        newpath = path[:i + 1]
        return newpath + list(reversed((path[i + 1:])))
    else:
        return None