I was just wondering if someone amongst us are working on linear algebra/matrix theory and graph theory....I have four (make that three as one already dropped the course) special problem students working on the eigenvalues of special classes of graphs (as obtained using certain operations on labeled graphs) as defined in the book by Kelp and Knauer... The main question I have is this...what happens if after generating a finite number of examples/graphs involving vertices and edges of Paths and/or Cyclesand still no pattern can be found ---would this be a case that bounds the unsolvable? Specially that most of the software being used by my students can only compute up to 25x25 vertices limiting their samples to a around 8-10 vertices (per class of Path or Cycle)...
The main reason is that they have barely three months to find results and failure to do so means they will have to extend for at least a semester (or at most two semesters) to finish the said course (MATH 190-Special Problem)..
Advance thanks for those who will respond...
What exactly do you mean in the bold part? Do you mean the special classes of graphs you're looking at are path graphs P_n and cycle graphs C_n? If you look at small examples of those I'm sure you'll find a pattern.
I was just wondering if someone amongst us are working on linear algebra/matrix theory and graph theory....I have four (make that three as one already dropped the course) special problem students working on the eigenvalues of special classes of graphs (as obtained using certain operations on labeled graphs) as defined in the book by Kelp and Knauer... The main question I have is this...what happens if after generating a finite number of examples/graphs involving vertices and edges of Paths and/or Cyclesand still no pattern can be found ---would this be a case that bounds the unsolvable? Specially that most of the software being used by my students can only compute up to 25x25 vertices limiting their samples to a around 8-10 vertices (per class of Path or Cycle)...
The main reason is that they have barely three months to find results and failure to do so means they will have to extend for at least a semester (or at most two semesters) to finish the said course (MATH 190-Special Problem)..
Advance thanks for those who will respond...