https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:16087 Tue 24 Aug 2021 14:27:30 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:50117 a be two positive integers. We say that G has all [a, b]-factors if G has an h-factor for every h: V→ N such that a≤ h(v) ≤ b for every v∈ V and ∑v∈Vh(v)≡0(mod2). A spanning subgraph F of G is called an (a, b)-parity factor, if dF(v) ≡ a≡ b (mod 2) and a≤ dF(v) ≤ b for all v∈ V. In this paper, we have developed sufficient conditions for the existence of all [a, b]-factors and (a, b)-parity factors of G in terms of the independence number and connectivity of G. This work extended an earlier result of Nishimura (J Graph Theory 13: 63–69, 1989). Furthermore, we show that these results are best possible in some cases.]]> Tue 11 Jul 2023 15:47:27 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:31313 n,k,m be three positive integers such that k=⎣(n - 1)/2⎦ and m≤k, we show that every 2k-regular m-edge-connected graph with 2n vertices contains at least m edge-disjoint perfect matchings, and the condition on edge connectivity is sharp.]]> Sat 24 Mar 2018 08:43:31 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:10371 Sat 24 Mar 2018 08:08:50 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:17310 Sat 24 Mar 2018 08:01:51 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:22971 n with connectivity κ(G)≤k and minimum degree δ(G)≥k. We show that among the graphs in this family, the maximum spectral radius is obtained uniquely at K_k+(K_δ−k+1∪K_n−δ−1). Another family of the graphs we study is the family of bipartite graphs with order n and connectivity k. We show that among the graphs in this family the maximum spectral radius is obtained at a graph modified from K_{⌊n/2⌋,n−1−⌊n/2⌋}. The third family of graphs we have studied is the family of graphs with order n, connectivity k and independence number r. We determine the graphs in this family that have the maximum spectral radius.]]> Sat 24 Mar 2018 07:15:20 AEDT ]]>