And also you should answer the main question , how will you find the automorphism function? Or how would you use the theorem only to decide if there exists an isomorphism?
2009/7/16 Miroslav Balaz <gpsla...@googlemail.com> > I think that there is logical error, in the proof what do you think about > it? > f(A)=B iff A and B have the same labelig, but what if there are 3 vertices > with the same labeling? say A,B,C > then F(A)=B and F(A)=C > > you forget to quantify the f. I think everyone stops reading it if you will > have such errors there. > > 2009/7/15 mimouni <mimouni.moha...@gmail.com> > > >> you can consult in: http://www.wbabin.net/science/mimouni2e.pdf >> and I finished on implimentation schedule a php (to find the labels >> for a graph exceeds 5000 vertices). >> >> On 14 juil, 19:25, Miroslav Balaz <gpsla...@googlemail.com> wrote: >> > Graph isomorphism is not very good problem, because for human generated >> > graphs the algorithhm for tree-isomprphism wlll work. >> > But that is only my personal opinion. >> > >> > But it is hard to understand your algorithm. >> > Mainly because i do not understand the words you are using >> > peak-? >> > summit-? >> > pseudo tree-? >> > stoppage-? >> > nhbm-? >> > Also you have there a lot of errors( i do not mean englis erros) >> > You should rework that, i was rewriting my master's thesis proofs at >> least 3 >> > times each. >> > >> > 2009/7/14 mimouni <mimouni.moha...@gmail.com> >> > >> > >> > >> > >> > >> > > Hello, I found a new labeling vertex, which can make the deference >> > > between the peaks of a graph, and thus resolve the automorphism and >> > > isomorphism. Its complexity is estimated to O (n^3). >> > > And here is the procedure: >> > > To build a pseudo tree this way: >> > > 1. Put a single vertices (example: A) in the Level 1. >> > > 2. Putting all the peaks surrounding the vertices An in Level 2. And >> > > not forgetting the edges. >> > > 3. Putting all the peaks adjacent to each vertex exists in the >> > > nouveau2, and without duplication and without forgetting the edges. >> > > In >> > > the level 3. >> > > 4. Repeat Step 3 until more vertices. >> > > Labeling the vertices; is therefore in this way: >> > > 1. in built all the pseudo trees. >> > > 2. In seeking pseudo tree that’s a vertices lies in the level x. >> > > 3. Labeling the vertices in the A-level x is composed of four parts: >> > > the number of times or A lies in the level x, the total number of >> > > stoppages A up, the total number of stoppages in the same A level, >> > > and >> > > finally the total number of stoppages A down. >> > > 4. And labeling a vertex is the labeling on all levels. >> > > Making the deference between A and B. >> > > the two vertices A and B are isomorphism between waters if they both >> > > have the same labeling. >> > > If the labeling of A in a level x is deferential to the labeling of B >> > > at the same level, then A and B are deferens. >> > > ======================== >> > > Validity of the algorithm >> > > The demonstration validation of this algorithm is trivial! >> > > Theorem Let A and B, two peaks in a graph G. function of the >> > > automorphism of G to G is noted f. >> > > f (A) = B if and only if, A and B have the same labeling. >> > > Proof 1) f (A) = B. >> > > Here we will show that A and B on the same labeling. Let x and two >> > > other top graph G, such that f (x) = y. Labeling is based on pseudo- >> > > tree, so if the tree with pseudo-header as x, A is in the p, and B is >> > > in the level q. then the automorphism keeps the distance, then: >> > > For the pseudo-tree with it as header, B is in the p, and A is in the >> > > level q. >> > > With the same idea was for the pseudo-tree x, adjacent to A summits >> > > are divided into three parts (top, at the same level as A, and >> > > bottom), then the pseudo-tree there, the adjacent peaks B are also >> > > divided into three parts (top, at the same level as B, and bottom). >> > > So the two summits: A and B have the same labeling >> > > 2) A and B have the same labeling. >> > > If the labeling of A in the pseudo-tree x is nhmb, labeling B in the >> > > pseudo-tree is also: n hmb because it af (x) = y. with the same idea >> > > (the automorphism keeps distance), we find that f (A) = B. >> > > So: f (A) = B if and only if, A and B have the same labeling. >> > > Complexity of the algorithm >> > > the complexity of a pseudo-tree is O(n²). >> > > the complexity of all pseudo is so O(n³). >> > > the complexity of labeling a summit from a pseudo-tree is O(n). >> > > the complexity of the labeling is a summit O(n²). >> > > So the algorithm is polynomial >> > > ======= >> > > implementation >> > > an application in beta (for small graphs) in php is available on: >> > >http://mohamed.mimouni1.free.fr/ >> > > and for big graphs is avaibles on: >> > >http://sites.google.com/site/isomorphismproject/ >> >> >> >> > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/algogeeks -~----------~----~----~----~------~----~------~--~---
