IFCAM=Indo French Centre for Applied Mathematics

This is a project on **application of graph homomorphisms on graph database**.

I am the coordinator for French site and Sagnik Sen is the coordinator for Indian site.

Members of project:

**French side:**

- Julien Bensmail,
- Florent Foucaud,
- Amélie Gheerbrant,
- Dimitri Lajou,
- Reza Naserasr
*(coordinator of French side)* - Theo Pierron,
- Cristina Sirangelo,
- Eric Sopena,

**Indian side:**

- Sandip Das,
- Subir K. Ghosh,
- Dibyayan Chakraborty,
- Harmender Gahlawat,
- Joydeep Mukherjee,
- Swathy Prabhu,
- Uma kant Sahoo,
- Sagnik Sen
*(coordinator of Indian side)*

**Summary of the project:**

In this project, we are going to study the graph homomorphism problems from a very general point of view. Apart from studying the usual graph homomorphism on undirected graphs, we will study it for different types of graphs such as, signed graphs, oriented graphs, edge-colored graphs, colored mixed graphs etc. We will apply the theories and techniques associated with graph homomorphism to solve practical problems. Our main application oriented work is studying graph homomorphism in the context of graph database, a type of database now a days used even by popular social medias. Graph homomorphism is equivalent to the query evalution problem in graph database, and thus have exciting intersection with the theory. In our group we have experts of graph homomorphisms as well as graph database making this project a potential case for Indo- French interdeciplinary collaboration. We want to organize a workshop by the end of this project. We also consider a few other application oriented topics as auxiliary research tracks inside this project.