An investigation of combinatorial problems

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Searching for intruders in graphs (networks) is one of the problems I shall be studying.  I shall be considering certain families of graphs with a view towards determining the minimum number of searchers required, or the minimum time required for a fixed number of available searchers. Another topic of investigation is graph decompositions.  This is a continuation of work I have been doing for many years.  Some of the results have applications in scheduling. The final broad topic of investigation is Cayley graphs.  These are graphs that are constructed using groups.  They possess a large amount of symmetry which makes them useful in some surprising applications.  I'll be looking at them mainly from the subgraph point of view and isomorphism point of view.