The document is a presentation by Pritam Chandra Shil on isomorphism, derived from Greek terms meaning 'equal form or shape'. It explains the concept of graph isomorphism, detailing conditions for two graphs to be isomorphic and its applications in organic chemistry. The document also touches on the complexity of the graph isomorphism problem and its classification in NP.

1. Welcome To My
Presentation

2. SUBMITTED BY
PRITAM CHANDRA SHIL
ID: 162-15-7882
Topic -> Isomorphism

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."
Formally , an isomorphism
is bijective morphism.

4. Graph Isomorphism
 Two graphs G=(V,E) and H=(W,F) are isomorphic
if there is a bijective function f:
V -> W such that for all v , w € F
-{ v , w} € { f (v) , f(w)} € F

5. Variant for labeled graphs
 Let G= (V,E) , H=(W,F) be graph with vertex
labelings l: V -> L , l’ -> L.
 G and H are isomorphic labeled graphs, if there is
a bijective function f: V -> W such that
- for all v , w € V: (v , w) € E < - >{f(v),f(w)} € F
- for all v € V : l(v) = l’ (f(v)).
 Application organic chemistry :
- determining if two molecules are identical.

6. Complexity of graph isomorphism
 Problem is in NP , but
- NO NP- completeness proof is known
- NO polynomial time algorithm is known
If P≠NP G.Isomorphism
NP-complete
PNP

7. Isomorphism: The structure of 2 trees
are equal.

8. How to Judge two rooted trees are
isomorphic ??

9. Eliminate & Rebuild

10. THANK YOU !!