https://ogma.newcastle.edu.au/vital/access/ /manager/Index en-au 5 HSAGA and its application for the construction of near-Moore digraphs https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:4975 Wed 11 Apr 2018 09:35:56 AEST ]]> Discrete algorithms and methods for security of statistical databases related to the work of Mirka Miller https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:36069 Tue 04 Feb 2020 11:12:06 AEDT ]]> Breaking the 2ⁿ-barrier for irredundance: two lines of attack https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12245 Sat 24 Mar 2018 08:08:09 AEDT ]]> Power domination in certain chemical structures https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:27629 γp(G). In this paper, we establish a fundamental result that would provide a lower bound for the power domination number of a graph. Further, we solve the power domination problem in polyphenylene dendrimers, Rhenium Trioxide (ReO3) lattices and silicate networks.]]> Sat 24 Mar 2018 07:34:26 AEDT ]]> Maximum spectral radius of graphs with given connectivity, minimum degree and independence number https://ogma.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 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 ]]>