# Algorithms for Finding Isomorphic Subgraphs.

## Date of Submission

December 2001

## Date of Award

Winter 12-12-2002

## Institute Name (Publisher)

Indian Statistical Institute

## Document Type

Master's Dissertation

## Degree Name

Master of Technology

## Subject Name

Computer Science

## Department

Applied Statistics Unit (ASU-Kolkata)

## Supervisor

Roy, Bimal Kumar (ASU-Kolkata; ISI)

## Abstract (Summary of the Work)

In general subgraph isomorphism problem, given a ext G and a pattern H, one must either detect an occurrence of H as a subgraph of G, or list all oc- currences of H as a subgraph of G. The subgraph isomorphism problem consists in deciding for two given graphs whether one graph is isomorphic to a subgraph of other, i.e., whether there is a bijective mapping from the vertex set of one graph to a subset of vertex set of second graph such that the edge connections are preserved. This problem is of considerable practical, as well as theoretical, importance. Theoretically, subgraph isomorphism is a common generalization of many important graph problems including finding Hamiltonian paths, cliques, matchings, girth, and shortest paths [9]. Vari- ations of subgraph isomorphism problem have been used to model various practical problems such as molecular structure comparison (1), integrated circuit testing (5], microprogrammed controller optimization [12], analysis of Chinese ideographs [13). robot motion planning (14], semantic network retrieval (15), and polyhedral object recognition (18). One of the possible applications of subgraph isomorphism is, for given the structural formulas of chemical compounds, to finding whether a chemical compound is a subcom- pound of another compound (7). Subgraph isomorphism may be useful in scene analysis for detecting a relationally described object that is embedded in a scene (2,17).In this report we are mainly concentrated on the occurrences of a graph in another graph. In section 2 we have mentioned some results for different class of graphs which are deciding atleast one occurrence of a graph as a subgraph of another graph. But the number of occurrence may be more than one. In section 3 we have considered the problem of distinct occurrences a graph in another graph and proved that both decision and optimal version of this problem is NP-complete. An algorithm, for finding all but not distinct occurrences of a graph as a subgraph of another graph, is discussed in section.

## Control Number

ISI-DISS-2001-81

## Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

## DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/6253

## Recommended Citation

Giri, Pradeep Kumar, "Algorithms for Finding Isomorphic Subgraphs." (2002). *Master’s Dissertations*. 85.

https://digitalcommons.isical.ac.in/masters-dissertations/85

## Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843099