example of a triangle: A-B A-C A-B here it is clear that the vertex A, B and C have identical labeling.
On 16 juil, 18:19, Miroslav Balaz <gpsla...@googlemail.com> wrote: > 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. 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