Degree Diameter Problem on Oxide Network

The degree diameter problem is the problem of finding the largest graph (in terms of number of vertices) subject to the constraints on the degree and the diameter of the graph. Beyond the degree constraint there is no restriction on the number of edges (apart from keeping the graph simple) so the resulting graph may be thought of as being embedded in the complete graph. In a generalization of this problem, the graph is considered to be embedded in some connected host graph. This article considers embedding the graph in the oxide network and provides some exact values and some upper and lower bounds for the optimal graphs.