Isomorphism Graph
- 1. WELCOME TO MY PRESENTATION •Isomorphism • Submitted To • Md.Sadikur Rahman • Submitted By • Md. Rakib Hasan • Id: 162-15-7802
- 2. TODAY’S TOPICS: --GRAPH ISOMORPHISM: DEFINITION -EXAMPLE OF ISOMORPHIC GRAPH -ISOMORPHISM FOR TREES Rooted trees Unrooted trees
- 3. WHAT IS ISOMORPHISM ?? • Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or "to shape.“ " is isomorphic to " is written ." is isomorphic to " is written
- 4. EXAMPLE OF GRAPH ISOMORPHISM • In the graph G3, vertex ‘w’ has only degree 3, whereas all the other graph vertices has degree 2. Hence G3 not isomorphic to G1 or G2
- 5. ISOMORPHISM EXAMPLE IF ISOMORPHIC , LEVEL THE 2ND GRAPH TO SHOW THE ISOMORPHISM , ELSE IDENTIFY DIFFERENCE
- 6. ISOMORPHISM ON TREES LINEAR TIME ALGORITHM TO TEST IF TWO (LABELED) TREES ARE ISOMORPHIC. ULLMAN, 1974) ALGORITHM TO TEST IF TWO ROOTED TREES ARE ISOMORPHIC. USED AS A SUBROUTINE FOR UNROOTED TREES.
- 7. ROOTED TREE ISOMORPHISM FOR A VERTEX V IN T, LET T(V) BE THE SUBTREE OF T WITH V AS ROOT. LEVEL OF VERTEX: DISTANCE TO ROOT. IF T1 AND T2 HAVE DIFFERENT NUMBER OF LEVELS: NOT ISOMORPHIC, AND WE STOP. OTHERWISE, WE CONTINUE:
- 8. UNROOTED TREES CENTER OF A TREE A vertex v with the property that the maximum distance to any other vertex in T is as small as possible. Each tree has a center of one or two vertices. FINDING THE CENTER: Repeat until we have a vertex or a single edge: Remove all leaves from T. O(n) time: each vertex maintains current degree in variable. Variables are updated when vertices are removed, and vertices put in set of leaves when their degree becomes 1.