Adjunct Professor (Since April 2009)

Department of Mathematics

(From June 2014)

**Chair in Discrete Mathematics (2005 - 2009) **
Department of Science and Technology (DST)

Srinivasan Ramanujan Centre,SASTRA University, Kumbakonam

Bharathidasan University, Tiruchirappalli

Annamalai University, Annamalainagar

Department of Mathematics

National College, Tiruchirappalli-620001

Algebraic Graph Theory

Graph Coloring

1. (with N. Ramabhadran) A Textbook of Modern Algebra, Vikas Publishing House, New Delhi.

2. (with K. Ranganathan) A Textbook of Graph Theory, Springer, New York. (Second Edition), 2012.

3. (with S. Sridharan) Discrete Mathematics (under preparation).

1. Proceedings of the Ramanujan Centennial International Conference held at Annamalai University
in December 1987; published by the Ramanujan Mathematical Society.

2. Proceedings of the International Conference on Discrete Mathematics held at Tiruchirappalli in
January 1996. Proceedings was published as Vol. 206 (August 1999) of the North Holland (now
Elsevier) Journal: Discrete Mathematics.

3. Proceedings of the January 1998 Conference on Graph Connections held at Cochin University
of Science and Technology; published by M/s. Allied Publishers, India.

4. Proceedings of the March 2001 Conference on Graph Theory and its Applications, Anna
University, Chennai; published by Narosa Publishing House.

5. Proceedings of the International Conference on Discrete Mathematics, December 2006, held at
Indian Institute of Science, Bangalore; published under the RMS-LNS Lecture Notes Series
International Press, Boston.

6. Proceedings of the ICM 2010 Satellite Congress on Recent Trends in Graphs and Combinatorics
(ICRTGC - 2010)- Discrete Mathematics 312 ( 2012).

The Energy of a Graph, Linear Algebra and its Applications, 387(2004), 287-295.

(With N. Sridharan and K. Viswanathan Iyer) The Weiner Index of Odd Graphs, Journal of
Indian Institute of Science, 86 (2006), 527-531.

(With K. Viswanathan Iyer and K.T. Raghavendra) Weiner Index of two special tress, MATCH Communications, Math. Comput. Chem. 57(2007), 385-392.

(With N. Sridharan and K. Viswanathan Iyer) A Sharp lower bound for the Weiner Index of a graph, Ars Combinatoria, 2011.

(with C. Adiga and Wasin So) The Skew Energy of a Digraph, Linear Algebra and its Applications, 432(2010), 1825-1835.

(with T. Kavaskar and Wasin So) The energy of the Mycielskian of regular graphs, Australasian Journal of Combinatorics, 52 (2012), Pages 163–171.

(with S. Francis Raj) Connectivity of the Mycielskian of a Graph, Discrete Mathematics, 308(2008), 2607-2610.

(with S. Francis Raj) The Wiener number of Kneser Graphs, Discussiones Mathematicae Graph Theory, 28(2008), 219-228.

(with S. Francis Raj) Bounds for the b-chromatic Number of Vertex Deleted Subgraphs and the Extremal Graphs, Electronic Notes in Discrete Mathematics, 34(2009), 353-358.

(with S. Francis Raj) The Wiener Number of Powers of the Mycielskian, Discussiones Mathematicae Graph Theory, 30 (2010).

(with S. Francis Raj) Bounds for the b-chromatic Number of the Mycielskian of some families of graphs, to appear in ARS Combinatoria.

(with S. Francis Raj) Bounds for the b-chromatic number of G-v, to appear in Discrete Applied Mathematics (2012).

(with T. Kavaskar) Fall Coloring of Graphs-I, Discussiones Mathematicae Graph Theory, 30 (2010), 385-391.

(with T. Kavaskar) Fall Coloring of Graphs-II, Journal of Combinatorial Mathematics and Combinatorial Computing, 76 (2011), 21-31.

(with T. Kavaskar) Color Chain of a Graph, Graphs and Combinatorics, 27 (2011), 487-493.

(with T. Kavaskar) b-coloring of Kneser graphs, Discrete Applied Mathematics, 160 (2012), 9-14.

(with T. Kavaskar) Interpolation theorem for partial Grundy coloring, Discrete Mathematics, 313 (2013) 949–950.

(with S. Francis Raj and T. Kavaskar) b-Chromatic Number of Cartesian Product of Some Families of Graphs, to appear in Graphs and Combinatorics

(with S. Francis Raj and T. Kavaskar) b-coloring of Cartesian product of odd graphs, to appear in ARS Combinatoria.

(with A. Anuradha) Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube, Proceedings of the International Workshop and Conference on Combinatorial Matrix Theory and Generalized Inverses of Matrices-2012, Springer.

(with A. Anuradha, Xiaolin Chen, Xueliang Li, Huishu Lian and Wasin So) Skew Spectra of Oriented Bipartite Graphs, The Electronic Journal of Combinatorics, 20 (4) (2013) P18.

(with A. Anuradha and Wasin So) Skew Spectra of Graphs Without Even Cycles, Linear Algebra and its Applications, 444 (2014) 67-80.

(with A. Anuradha and G. Indulal) Some new families of integral graphs, to appear in Indian Journal of Pure and Applied Mathematics (Springer).

**One of the principal organizers for the following: **

1. Ramanujan Centennial International Conference, 1987, held at Annamalai University.

2. International Conference on Number Theory and Discrete Mathematics 1996, held at
Tiruchirappalli.

3. International Conference on Discrete Mathematics ICDM 2006, held at Indian Institute of
Science, Bangalore.

4. International Conference on Discrete Mathematics ICDM 2008, held at University of Mysore,
Mysore.

5. International Conference on Discrete Mathematical Chemistry, (2007) Bangalore.

6. International Conference on Discrete Mathematical Chemistry, (2008) Kalapet, Kerala.

7. First India-Taiwan Conference in Discrete Mathematics, November 2009, Taipei, Taiwan.

8. International Workshop on Graph Coloring 2010, Bharathidasan University, Tiruchirappalli.

9. Second India - Taiwan Conference on Discrete Mathematics, Amrita University, Coimbatore,
September 8-11, 2011.

10. Third India - Taiwan Conference on Discrete Mathematics held in National Chiao
Tung University, Taiwan during November 18-22, 2013.

1. Founder - Secretary of the Ramanujan Mathematical Society

2. Life Member of Ramanujan Mathematical Society, Indian Mathematical Society, American
Mathematical Society and Academy of Discrete Mathematics and Applications (ADMA).

3. Chief Editor of Mathematics Newsletter from 1991 to 2004, published by the Ramanujan
Mathematical Society and sponsored by the National Board for Higher Mathematics, India.

1) N. Sudharsanam

2) K. Ranganathan

3) P. Paulraja

4) A. Rahim Basha

5) V. Yegnanarayanan

6) R. Sampathkumar

7) A. Selvam

8) S. Francis Raj

9) T. Kavaskar

10) A. Anuradha

**Prof. R.Balakrishnan **

Adjunct Professor

Department of Mathematics

Bharathidasan University

Tiruchirappalli-620024

India

Mobile: 09865016756

**E-mail:**** mathrb13@gmail.com**

Bharathidasan University,
Tiruchirappalli, India