In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizh...In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizhong Zhou,Hongxia Liu and Yang Xu(2022).Then,an A_(α)-spectral condition is given to ensure that G is a fractional ID-[a,b]-factor-critical covered graph and an(a,b,k)-factor-critical graph,respectively.In fact,(a,b,k)-factor-critical graph is a graph which has an[a,b]-factor for k=0.Thus,these above results extend the results of Jia Wei and Shenggui Zhang(2023)and Ao Fan,Ruifang Liu and Guoyan Ao(2023)in some sense.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961041,12261055)the Key Project of Natural Science Foundation of Gansu Province(Grant No.24JRRA222)the Foundation for Innovative Fundamental Research Group Project of Gansu Province(Grant No.25JRRA805).
文摘In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizhong Zhou,Hongxia Liu and Yang Xu(2022).Then,an A_(α)-spectral condition is given to ensure that G is a fractional ID-[a,b]-factor-critical covered graph and an(a,b,k)-factor-critical graph,respectively.In fact,(a,b,k)-factor-critical graph is a graph which has an[a,b]-factor for k=0.Thus,these above results extend the results of Jia Wei and Shenggui Zhang(2023)and Ao Fan,Ruifang Liu and Guoyan Ao(2023)in some sense.
