Brief Profile
With the help of God, family, society and the nation I could achieve the following.
1. Gifted to work as the Head of Department of Mathematics for 36½ years - 33½ years at St. Jude’s College, Thoothoor (SJCT) (at my native place) and 3 years at CU Kerala and again took charge as HoD on 30.09.2022; 5 years as Vice Principal and one-year Principal-IC at SJCT successfully.
2. Have more than 40 years of continuous service as Lecturer/Senior Lecturer/ Selection Grade Lecturer/Reader/Associate Professor/Professor - at SJCT 33½ years (12.07.1982 to 09.12.2015) and at CU Kerala from 10.12.2015 onwards.
3. 6 Ph.D. candidates and 8 M.Phil. candidates successfully completed their degrees under my guidance.
4. Published 27 research papers.
5. My h-index is 10; i10-index is 11 & Citations 391.
6. Completed two minor UGC projects for Rs. 60,000/- and Rs. 1,00,000/- and a DST-SERB major project for Rs.10,81,200/-.
7. Obtained 100% in Mathematics in university exams in PUC, B.Sc. I & II years and in one paper (Incompressible Fluid Flow) in M.Sc. (Appl. Maths).
8. Played mathematics and foot-ball at IIT, Bombay as Senior Research Fellow (SRF) from 09.12.1980 to 01.10.1981.
9. I could produce more than 1600 responsible (mathematicians/) students/citizens at SJCT and at CU Kerala. Hundreds of our students are working in USA, Europe and in Gulf countries.
10. Solved a 1962 Conjecture on the existence of self-complementary circulant graphs, stated by Horst Sachs of Germany.
11. Defined Sigma labeling (Distance Magic labeling) of graphs and Type-2 isomorphism (a new type of isomorphism) among circulant graphs and developed their theories.
12. Developed a new theory on Cartesian product and factorization of circulant graphs similar to product and factorization of natural numbers.
13. Have combined publications with two leading mathematicians, Prof. Lowell W. Beineke, Purdue University, USA and Prof. Brian Alspach, University of Newcastle, Australia.
14. Membership:
i. Reviewer of Mathematical Review of AMS (reviewed 146 papers).
ii. Reviewer of Advances in Science, Technology and Engineering Systems Journal.
iii. American Mathematical Society (AMS No. KMVLXB/VLVXXC)-Member from 1997 (sponsored by Prof. Lowell W. Beineke, Indiana-Purdue Univ., U.S.A.).
iv. Society for Industrial and Applied Mathematics (SIAM) - Member from 2013.
v. Ramanujan Mathematical Society (RMS) - Life member.
vi. Academy of Discrete Mathematics & its Applications (ADMA) - Life member.
vii. Kerala Mathematical Association (KMA) - Life member.
viii. Indian Mathematical Society (IMS) – Life member.
ix. Orcid ID: https://orcid.org/0000-0002-3430-5043
x. Web of Sci ID: ABC-9235-2021
xi. Vidwan ID: 60325
Recent and Major Publications
- V. Vilfred Kamalappan,"A survey of two types of labelings of graphs",Discrete Mathematics Letters,Vol. No. 6
Page 8-18.
- ,"On Several New Contiguous Function Relations for k-Hypergeometric Function with Two Parameters",Communications of the Korean Mathematical Society,2017
- ,"(a, d)-continuous monotonic subgraph decomposition of K_(n+1) and integral sum graphs G_(0,n)",Tamkang Journal of Mathematics,2015
- ,"Families of Circulant Graphs without Cayley Isomorphism Property with m_i = 3",IOSR (International Organization of Scientific Research) Journal of Mathematics,2019
- ,"A Study on (a, d)-antimagic graphs using partition",Journal of Combinatorial Mathematics And Combinatorial Computing,2011
- ,"New Families of Circulant Graphs without Cayley Isomorphism Property with m_i = 2",International Journal of Applied and Computational Mathematics (IJACM) - Springer,6, 90 (2020), 34 pages
- ,"A study on isomorphic properties of circulant graphs",Advances in Science, Technology and Engineering Systems Journal (ASTES) Journal,2 (6) (2017), 236-241
- ,"Families of Circulant Graphs without Cayley Isomorphism Property with m_i = 7 ",Journal of Mathematics of IOSR (International Organization of Scientific Research) Journal of Mathem,12 (2016), 32 - 37
- ,"Families of Circulant Graphs without Cayley Isomorphism Property with m_i = 5",Int. Journal of Scientific and Innovative Mathematical Research,3 (6) (2015), 39 - 47
- ,"A Few More Properties of Sum and Integral Sum Graphs",Journal of the Indonesian Mathematical Society ,20 (2) (2014), 149 - 159
- ,"Number of Cycles of Length Four in Sum Graphs G_n and Integral Sum Graphs G_{m,n} ",Int. Journal of Scientific and Innovative Mathematical Research,2 (4) (2014), 366 - 377
- ,"More Properties of Sum Graphs",Graph Theory Notes of New York, Mathematical Association of America,66 (2014), 10-15
- ,"A Theory of Cartesian Product and Factorization of Circulant Graphs (Provides a complete theory of Cartesian product and factorization of circulant graphs, similar to product and factorization of Natural numbers.)",Journal of Discrete Mathematics, Hindawi Publishing Corporation,Volume 2013, Article ID 163740, 10 pages
- ,"Integral sum graphs and maximal integral sum graphs ",Graph Theory Notes of New York, Mathematical Association of America,63 (2012), 28-36
- ,"Number of Triangles in Integral Sum Graphs G_{m,n}",Int. J of Algorithms, Computing and Mathematics,4 (2011), 16-24
- ,"Banana Trees and Union of Stars are Integral Sum Graphs",Ars Combinatoria,102 (2011), 79-85
- ,"Amalgamation of Integral sum graphs, Fan and Dutch m-windmill are integral sum graphs",Graph Theory Notes of New York, Mathematical Association of America,58 (2010), 51-54
- ,"Odd Anti-magic and Odd (a, d)-antimagic graphs",IJ of Algorithms, Computing and Mathematics,3 (2010), 47-54
- ,"The integral sum graph G_{\Delta n}",Graph Theory Notes of New York, Mathematical Association of America,57(2009), 43-47
- ,"Interchange similar self-vertex switchings in graphs",J. of Discrete Math. Sci. and Crypt.,12 (2009), 467-480
- ,"Branches and Joints in the study of self-switching of graphs ",JCMCC (Journal of Combinatorial Mathematics and Combinatorial Computing),67(2008), 111-122
- ,"Sigma Partition and Sigma Labeled Graphs",Journal of Decision and Mathematical Sciences ,10 (2005), 1–12
- ,"On (a, d) Anti-magic special trees, unicyclic graphs and complete bipartite graphs ",Ars Combinatoria,70 (2004), 207-220
- ,"Classes of Prime Labeled Graphs",IJOMAS (International Journal of Management and Systems) ,18 (2002), 217-226
- ,"Some results on sum graphs",Journal of Combinatorics, Information and System Sciences ,26 (2001), 135-142
- ,"Families of Graceful Banana Trees",IJOMAS (International Journal of Management and Systems),15 (1999), 275-286
- ,"Self-complementary circulant graphs",Ars Combinatoria,53 (1999), 187-191
- ,"Sigma Labeling and Circulant Graphs (My Ph.D. thesis)",Lambert Academic Publishing, Germany,22-04-2020
Research Projects Undertaken
A study on properties of sum graphs and integral sum graphs.
DST (SERB): SR/S4/MS:679/10
Major Project: DST (SERB): SR/S4/MS:679/10
A study on sum and integral sum labelings.
UGC (SERO): MRP-684/2005
A study on integral sum graphs.
UGC (SERO)
Books / Chapters
Chapter(s) - Co-Author, (2010). Algebra, Graph Theory and their Applications, Narosa Publishing House, New Delhi, India., ISBN 978 -81-8487-0669-5Chapter(s) - Sole Author, (2004). Graph Theory and its Applications, Narosa Publishing House, New Delhi, India., ISBN 81-7319-569-2Book - Co-Author, (2013). ICAMTCS 2013: Proceedings Volume-I, Bonfring, Coimbatore, Tamil Nadu, India., ISBN 978-93-82338-30-7
Miscellaneous
| Membership/Fellowship of other institutions/professionals societies : |
i. Reviewer of Mathematical Review of AMS (MR Reviewer No. 073139). - Reviewed 146 papers.
ii. Reviewer of Advances in Science, Technology and Engineering Systems Journal (ASTESJ Reviewer No. RVMAP0001).
iii. American Mathematical Society (AMS No. KMVLXB)-Member from 1997 (sponsored by Prof. Lowell W. Beineke, Indiana-Purdue Univ., U.S.A.).
iv. Society for Industrial and Applied Mathematics (SIAM No. 001071639)- Member from 2013.
v. Ramanujan Mathematical Society (RMS) - Life member. Membership No. 441.
vi. Academy of Discrete Mathematics & its Applications (ADMA) - Life member.
vii. Kerala Mathematical Association (KMA) – Life member.
viii. Indian Mathematical Society (IMS No. V-061) – Life member.
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| Student related co-curricular, extension and field based activities and counseling. |
6 candidates completed their Ph.D. degrees at M.S. University, Tirunelveli, Tamil Nadu under my guidance.
1. Dr. L. Mary Florida, Ph.D. Reg. No. 1483: A Study on Graph Labeling Problems and Packing of Graphs. 17.07.2006
2. Dr. C. Jayasekaran, Ph.D. Reg. No. 761: A Study on Self Vertex Switching of Graphs. 11.04.2008
3. Dr. J. Sivasakthivel, Ph.D. Reg. No. 1973: Time Series Analysis – An application to price forecasting. 07.07.2010
4. Dr. A. Suryakala, Ph.D. Reg. No. 3087: A Study on Sum and Integral Sum Labeling and Decomposition of Graphs. 30.06.2014
5. Dr. K. Rubin Mary, Ph.D. Reg. No. 3210: A Study on Properties of Sum and Integral Sum Graphs. 26.08.2016
6. Dr. P. Wilson, Ph.D. Reg. No. 5404: A Study on Isomorphic Circulant Graphs. 16.10.2017
And presently I am guiding 3 research candidates at CUK.
Guided 8 M.Phil. candidates of M. S. University, Tirunelveli, Tamil Nadu.
(i) Miss X. Jasmine Jesi, Reg. No. A3561035-2004;
(ii) Miss M. Sorna Sankari, Reg. No. A3561043-20
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| Contribution to corporate sector-management of the department and institution through participation in academic and administration,committees and responsibilities.
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1. Conducted CUCET2017 as Observer on May 17th and 18th 2017 in Calicut-1 test centre (Govt. Voc. H.S.S. for Girls, Nadakkavu).
2. Attended orientation programme in Planning and Management of Science Education for Heads of Science Departments of colleges from 11th March to 16th March 1985, conducted by NIEPA (National Institute of Educational Planning and Administration) at New Delhi.
3. Participated in the first Joint India – AMS Mathematical Meeting held during 17-20th Dec., 2003 at I.I.Sc., Bangalore.
4. Governing Council Member in St. Xavier’s Catholic Engineering College, Chunkankadai, Nagercoil, Tamil Nadu from 03.01.2014 for three years.
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| Other activities/Responsibilities : |
Attended many refresher/winter/summer courses and national / international workshops / symposiums at I.I.Sc., Bangalore / Harish Chandra Research Institute, Allahabad / Pondicherry Univ. / MK Univ. / Cochin Univ. / NITK, Surathkal / Madras Univ. / Annamalai Univ. / MS Univ., Tirunelveli / Univ. of Bombay / Kerala Univ.
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| Any other relevant information, if not given above : |
1. Senior Research Fellow (SRF) at IIT, Bombay, under the MHD Project from 09.12.1980 to 01.10.1981.
2. Board of Studies Member from 2018 to 2021 at CUSAT, Cochin for M.Sc. 5 years Integrated Course.
3. Board of Studies Member at Scott Christian College (Autonomous), Nagercoil, Tamil Nadu from 2020.
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Teaching & Research Guidance
- Discrete Mathematics:Post Graduate
- Discrete Mathematics:Post Graduate
- Operations Research:Post Graduate
- Algebra 2:Post Graduate
- Algebra 2:Post Graduate
- Complex Analysis:Post Graduate
- Complex Analysis:Post Graduate
- Complex Analysis:Post Graduate
- Complex Analysis:Post Graduate
- Elementary Number Theory and Basic Algebra:Post Graduate
- Elementary Number Theory and Basic Algebra:Post Graduate
- Theory of Equations, Analytical Geometry of 3 Dimension, Calculus, Differential Equations, Operations Research, Computer Programming, Fortran Programming, Linear Algebra, Numerical Analysis, Real Analysis, Complex Analysis:Under Graduate