Question: Why is this graph not a network?

February 06 2011 djordan99 0
Maple 14
0

Can anyone help me understand why the following happens?

N := GraphTheory[Digraph]({[1,3],[3,9],[9,27]});

GraphTheory[IsNetwork](N);

and

M := GraphTheory[Digraph]({[1,2],[2,4],[4,8]}); 

GraphTheory[IsNetwork](M);

both indicate that the graph is not a network.  On the other hand, for numbers n other than 2 and 3, Maple does recognize the graph {[1,n],[n,n^2],[n^2,n^3]} as a network.

This procedure that I wrote:

FindNetwork := proc()
  local G, N, b, i, m;
  for b from 2 to 100 do
    for m from 1 to 10 do
      G := {};
      for i from 0 to m do
        G := G union {[b^i,b^(i+1)]};
      end do;
      N := GraphTheory[Digraph](G);
      if not GraphTheory[IsNetwork](N,1,b^(m+1)) then
        printf("failed: %d^%d\n", b, m);
      end if;
    end do;
  end do;
end proc:

indicates that for b=2 and b=3, and any value of m, the graph is not a network, but it is for all other values of b and m, it is.

Can anyone please explain why?

Thanks.

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