مشخصات پژوهش

In this paper, we prove that there is no r-regular graph (r ≥ 2) with a unique perfect matching. Also we show that a 2r-regular graph of order n has at least (r−(rk−+1) k)rr−−kk−1n 2k-factors, where k ≤ r. We investigate graphs with a unique [a, b]-factor and among other results, we prove that a connected graph with minimum degree at least 2 and a unique [1, 2]- factor with regular components is an odd cycle.