Graphs and  Networks- Spectra and energy of graphs, graph operators and its dynamics, graph products, power domination , game domination and Real world networks.

History of Mathematics, Mathematics Education – Creative Mathematical Sciences Communication, Mathematics Popularisation.

a)Board of Studies in Mathematics, Cochin University of Science and Technology (1992-1995, 2000-2004, 2004-2008, Chairman : 2008-2012, 2013-2017, 2017-2021).

b)Academic Council of CUSAT (2001-2004, 2004-2006, 2006-2008, 2008-2012, 2012- 2017, 2017-2021). Member, Standing Committee of the Academic Council (2016- 2021).

c)Vice Chairman - Academic Committee for CBCS courses, CUSAT (2016 - 18).

d)Executive Council of the Ramanujan Mathematical Society (1998-2000, 2004-2006, 2006-2008, 2008-2010).

e)Academic Secretary (Founder) : Kerala Mathematics Teachers Association (an association for school teachers. (2001- 2017). President : 2017-

f)Academic Secretary, Ramanujan Mathematical Society, India (2002-2004).

g)Academic Secretary, Academy of Discrete Mathematics and Applications (2008- 2010, 2010-2012).

h)Member, Faculty of Mathematical Sciences, University of Delhi (2010-2013).

i)Member, Council of Indian Mathematical Society ( 2014-2017) .

j)Member, Executive Council, Association of Mathematics Teachers of India (2014- 

k)Chairman, Azim Premji University-Ramanujan Mathematical Society programmes for teachers training (2015-2019).

l)Member, Work Group on Higher Education, Kerala State Planning Board (2016).

m)Member, Academic Programme Committee, 5th India- Taiwan Conference on Discrete Mathematics, July 2017, Tamkang University, Taiwan

n)Member, Research Council , Kerala School of Mathematics, Calicut (2017-2021 ).

o)Vice President, Ramanujan Mathematical Society, India (2019- 2022).

p)Member, BOS in Mathematics, Amrita VisvaVidyapeetham, Coimbatore (2019-

q) President Elect, Academy of Discrete Mathematics and Applications (2024-2026)

• Indian Mathematical Society-Life Member (1985)

• Ramanujan Mathematical Society-Life Member( 1987)

• Association of Mathematics Teachers of India-Life Member (1980)

• American Mathematical Society-Member (1994-)

• Canadian Mathematical Society-Member (1999)

• Kerala Mathematics Teachers Association-Life Member (2001)

• Cryptology Research Society of India-Life Member(2006)

• Academy of Discrete Mathematics and  Applications-Life Member (2006-)

• Mathematical Association of America-Member (2007)

• Indian Science Congress Association-Life Member (2009-)

Honorary Director, Centre for InterdisciplinaryStudies , CUSAT (1999- 2003).

Head , Department of Mathematics CUSAT, 2001-2004; 2011- 2012, May 2016 – September 2017.

• Fellow (FTICA), The Institute of Combinatorics and its Applications , Canada (1999).

• Broad Outlook Learner Teacher Award of Air India (2007). 

Present Address: Emeritus Professor, Department of Mathematics,  Cochin University of Science and Technology,  Cochin-682022,  INDIA.
Tel : 0484-2577518,0484-2862461
E-mails : vijay@cusat.ac.in, vambat@gmail.com

Permanent Address: 'Pranavam', MNRA 130, 10th Cross Road, Maveli Nagar, Cochin-682 033.
Tel: 0484-2575288(R), Mob: 09447608851