/manager/Index ${session.getAttribute("locale")} 5 Note on parity factors of regular graphs /manager/Repository/uon:16087 Tue 24 Aug 2021 14:27:30 AEST ]]> On the number of disjoint perfect matchings of regular graphs with given edge connectivity /manager/Repository/uon:31313 n,k,m be three positive integers such that k=⎣(n - 1)/2⎦ and mk, 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 ]]> On superconnectivity of (4,g)-cages with even girth /manager/Repository/uon:10371 Sat 24 Mar 2018 08:08:50 AEDT ]]> On superconnectivity of (4, g)-cages /manager/Repository/uon:17310 Sat 24 Mar 2018 08:01:51 AEDT ]]> Maximum spectral radius of graphs with given connectivity, minimum degree and independence number /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 Kk+(Kδ−k+1∪Kn−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 ]]>