All Title Author
Keywords Abstract

Mathematics  2015 

A revised Moore bound for partially directed graphs

Full-Text   Cite this paper   Add to My Lib


The degree-diameter problem seeks to find the maximum possible order of a graph with a given (maximum) degree and diameter. It is known that graphs attaining the maximum possible value (the Moore bound) are extremely rare, but much activity is focussed on finding new examples of graphs or families of graph with orders approaching the bound as closely as possible. There has been recent interest in this problem as it applies to mixed or partially directed graphs, in which we allow some of the edges to be undirected and some directed. A 2008 paper of Nguyen and Miller derived an upper bound on the possible number of vertices of such graphs. We show that for diameters larger than three, this bound can be reduced and we present a revised Moore bound for mixed graphs valid for all diameters and for all combinations of undirected and directed degrees.


comments powered by Disqus

Contact Us


微信:OALib Journal