I obtained my Ph.D. (2008) in the field of Theoretical Computer Science. The title of my thesis is “Acyclic Edge Colouring: Bounds and Algorithms”. I carried out the research towards my Ph.D. at The Institute of Mathematical Sciences, Chennai, India under the guidance of Prof. C.R. Subramanian.

I worked under a post-doctoral fellowship at Laboratoire de Recherche en Informatique, Universite Paris Sud, Orsay, France (2009). I worked in a team headed by Prof. Yannis Manoussakis and conducted research in the field of Structures in Edge Coloured Graphs.

I currently work at DA-IICT and my broad research interests lie in the field of Graph Algorithms. I have guided one Ph.D. student, Mahipal Jadeja who defended his thesis (2018) titled “Set Labelling of Vertices and Study of Auxiliary Graphs”. I have also guided around ten M.Tech. Theses and several B.Tech. Projects.

My current research problems include:
-Defining auxiliary or other graph classes and/or obtaining mathematical characterizations and algorithms for them;
-Weight assignment to edges of complete graphs to yield a prespecified number of minimum weight spanning trees.

I teach courses in Theoretical Computer Science and Mathematics.

Graph Theory, Data Structures, Algorithms, Automata Theory

Conferences

• Rahul Muthu, N. Narayanan and C.R. Subramanian
  Improved bounds on Acyclic Edge Colouring
  Proceedings of the 2nd Brazilian Symposium on Graphs, Algorithms and Combinatorics, GRACO-2005, Electronic Notes in Discrete Mathematics, Volume 19, Pages 171-177.
• Rahul Muthu, N. Narayanan and C.R. Subramanian
  Optimal acyclic edge colouring of grid-like graphs
  Proceedings of the 12th Annual International Computing and Combinatorics Conference, COCOON-2006, Lecture Notes in Computer Science, Springer, volume 4112, pages 360-367.
• Rahul Muthu, N. Narayanan and C.R. Subramanian
  Acyclic Edge colouring of Outerplanar graphs
  Proceedings of the 3rd International Conference on Algorithmic Aspects in Information and Management, AAIM-2007, Lecture Notes in Computer Science, Springer, volume 4508, pages 144-152.
• Rahul Muthu, N. Narayanan and C.R. Subramanian
  k-intersection Colouring
  12th Workshop on Graph Theory; Colourings, Indepen- dence and Domination, CID 2007.
• V. Borozan, W. Fernandez de la Vega, Y. Manoussakis, C. A. Martinhon, R. Muthu and R. Saad
  Colored Trees in Edge-Colored Graphs
  8th CTW09, Paris, June 2009.
• Raquel Agueda, Valentin Borozan, Yannis Manoussakis, Gervais Mendy and Rahul Muthu
  Sufficient conditions for the existence of spanning colored trees in edge-colored graphs
  8th French Combinatorial Conference, Paris, June, 2010.
• R. Goyal, M. Jadeja, R. Muthu and B. Patel
  A New Characterisation of Total Graphs
  19th Japan-Korea Joint Workshop on Algorithms and Computation (WAAC 2016), Hakodate, Japan, 2016.
• M. Jadeja and R. Muthu
  Labeled Object Treemap: A New Graph-Labeling Based Technique for Visualizing
  Multiple Hierarchies
  19th Japan-Korea Joint Workshop on Algorithms and Computation (WAAC 2016), Hakodate, Japan, 2016.

Journals

• Rahul Muthu, N. Narayanan and C.R. Subramanian
  Improved bounds on acyclic edge coloring
  Discrete Mathematics, volume 307, number 23, 2007, pages 3063-3069.
• Rahul Muthu, N. Narayanan and C.R. Subramanian
  Optimal acyclic edge coloring of grid like graphs
  Discrete Mathematics 310 (21), 2769-2775.
• R Agueda, V Borozan, Y Manoussakis, G Mendy, R Muthu
  Sufficient conditions for the existence of spanning colored trees in edge-colored
  graphs
  Discrete Mathematics 312 (17), 2694-2699
• M. Jadeja, R. Muthu and V. Sunitha
  Set Labelling Vertices To Ensure Adjacency Coincides with Disjointness
  Electronic Notes in Discrete Mathematics vol. 63, pages 237-244
• M. Jadeja and R. Muthu
  Labeled Object Treemap: A New Graph-Labeling Based Technique for Visualizing
  Multiple Hierarchies
  Annals of Pure and Applied Mathematics, vol. 13, no. 1, pp. 49-62, January 2017.
• M. Jadeja and R. Muthu
  Uniform Set Labelling Vertices To Ensure Adjacency Coincides With Disjointness
  Journal of Mathematical and Computational Science, vol. 7, no. 3, pp. 537-553, May 2017.
• V. Borozan, W. Fernandez de la Vega, Y. Manoussakis, Rahul Muthu and Hong-Phong Pham
  Trees in Edge-Colored graphs
  European Journal of Combinatorics -Elsevier- (accepted and in press), 2018.

Preprints

• Rahul Muthu, N. Narayanan and C.R. Subramanian
  Acyclic Edge Colouring of Partial 2-Trees.
• Rahul Muthu and C.R. Subramanian
  Cartesian Products and Acyclic Edge Colouring.
• Rahul Muthu, N. Narayanan and C.R. Subramanian
  Some graph classes satisfying acyclic edge colouring conjecture.
• Abhishek Garg, Mahipal Jadeja and Rahul Muthu
  Spanning Tree Auxiliary Graphs.

• Data Structures
• Introduction to Graph Theory
• Formal Specification & Verification
• Approximation Algorithms
• Design & Analysis of Algorithms
• Graph Theory & Algorithms