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.
