4. The subgraph-isomorphism problem takes two graphs Gl and G2 and asks whetherGl is isomorphic to a subgraph of G2. Show thata) the subgraph-isomorphism problem is in NP; andb) it is NP-complete by giving a polynomial time reduction from SAT problem to it.Note: Two graphs G1=(V1, E1) and G2=(V2, E2) are isomorphic if there exists a one-one and onto function f( ) from V1 to V2 such that for every two nodes u and v in V1,(u,v) is in El if and only if (f(u), f(v)) is in E2. For examples, Gl is isomorphic to asubgraph with vertices {1,2,5,4} of G2 below.G1G2121234543

Actually, graph is a non linear data structure which consisting of nodes and edges.

4. The subgraph-isomorphism problem takes two graphs G1 and G2 and asks whether Gl is isomorphic to a subgraph of G2. Show that a) the subgraph-isomorphism problem is in NP; and b) it is NP-complete by giving a polynomial time reduction from SAT problem to it. Note: Two graphs GI=(V1, E1) and G2=(V2, E2) are isomorphic if there exists a one- one and onto function f( ) from V1 to V2 such that for every two nodes u and v in V1, (u,v) is in El if and only if (f(u), f(v)) is in E2. For examples, G1 is isomorphic to a subgraph with vertices {1,2,5,4} of G2 below. GI G2 1 1 2 3 5 3

4. The subgraph-isomorphism problem takes two graphs G1 and G2 and asks whether Gl is isomorphic to a subgraph of G2. Show that a) the subgraph-isomorphism problem is in NP; and b) it is NP-complete by giving a polynomial time reduction from SAT problem to it. Note: Two graphs GI=(V1, E1) and G2=(V2, E2) are isomorphic if there exists a one- one and onto function f( ) from V1 to V2 such that for every two nodes u and v in V1, (u,v) is in El if and only if (f(u), f(v)) is in E2. For examples, G1 is isomorphic to a subgraph with vertices {1,2,5,4} of G2 below. GI G2 1 1 2 3 5 3

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

4. The subgraph-isomorphism problem takes two graphs Gl and G2 and asks whether
Gl is isomorphic to a subgraph of G2. Show that
a) the subgraph-isomorphism problem is in NP; and
b) it is NP-complete by giving a polynomial time reduction from SAT problem to it.
Note: Two graphs G1=(V1, E1) and G2=(V2, E2) are isomorphic if there exists a one-
one and onto function f( ) from V1 to V2 such that for every two nodes u and v in V1,
(u,v) is in El if and only if (f(u), f(v)) is in E2. For examples, Gl is isomorphic to a
subgraph with vertices {1,2,5,4} of G2 below.
G1
G2
1
2
1
2
3
4
5
4
3

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