## Publications

K. Kayathri, On the size of edge-chromatic critical graphs, Graphs
and combinatorics(1994), 10:139-144.
S.A. Choudum and K. Kayathri, There are no edge-chromatic 4-critical graphs of order 12, Discrete mathematics, 141(1995)67-73.
S.A. Choudum and K. Kayathri, An extension of Vizing's adjacency lemma on edge-chromatic critical graphs, Discrete mathematics, 206(1995)97-103.
K. Kayathri and S. Pethanachi Selvam, Edge complete (p,2) semigraphs, Ars Combinatoria, 84(2007),65-76.
K. Kayathri and S. Pethanachi Selvam, Edge complete (p,3) semigraphs, Acta ciencia Indica, Vol XXXIII M, No. 2,(2007)621-631.
K. Kayathri and S. Pethanachi Selvam, Edge complete semigraphs, Proceedings of the international conference on mathematics and computer science, March 2007,53-73.
K. Kayathri and Mary Sunithi Vijayan, Coloring of complete semigraphs, Acta Ciencia Indica, Vol XXXIII M, No. 2,Dec (2007)605-614.
K. Kayathri and S. Pethanachi Selvam, Edge-complete (p,3) semigraphs, Journal of Mathematics and system sciences, vol. 3, Dec 2007, 621-631.
K. Kayathri and S. Pethanachi Selvam, Enumeration of one type of edge complete (p,3) semigraphs, Journal of algorithms computing and mathematics, vol. 3, Nov 2010,42-52.
K. Kayathri and S. Pethanachi Selvam, Enumeration of non-isomorphic semigraphs in gamma 4, ARS combinatoria, 2014.
K.Kayathri and J. Sakila devi, Supergraphs of 5-critical graphs, Proceedings of international conference on mathematics and its computational Applications, August 2014, 192-195
K.Kayathri and J. Sakila devi, Edge chromatic -critical graphs, Mathematical sciences International research journal, vol. 3, issue 2(2014) 658-662, ISSN 2278-8697
K.Kayathri and J. Sakila devi, Edge chromatic 5-critical graphs, International journal of fuzzy mathematical archieve, ISSN 2320-3242, vol. 7, Number 1,2,81-89,2015
K.Kayathri and J. Sakila devi, Structure of edge chromatic -critical graphs, Proceedings of the National Conference on Recent Developments on Emerging Fields in Pure and Applied mathematics, ISBN 978-93-83209-02-6,22-26,2015
K.Kayathri and J. Sakila devi, Edge chromatic 5-critical graphs of order 15, proceedia computer science, elesvier, volume 47, 332-336, 2015.
K.Kayathri and G.Kokilambal, Antipodal Domination in Graphs, Proceedings of the National Conference on Recent Developments on Emerging Fields in Pure and Applied mathematics, ISBN 978-93-83209-02-6,65-72,2015.
K.Kayathri and M.S.Chithra, 1-regular semigraphs with one and two m-vertices, Proceedings of the National Conference on Recent Developments on Emerging Fields in Pure and Applied mathematics, ISBN 978-93-83209-02-6,105-113,2015.
K.Kayathri and J.Shakila Jemima, Super Edge-Magic Total Labelings of Connected unicyclic (p,q) graphs with magic constant p+q+3, Advances in Theoretical and Applied Mathematics, ISSN 0973-4554, volume 11, Number 3(2016), pp. 261-274.
K.Kayathri and R.Amutha, Edge-Graceful Labelings of Connected Graphs, Electronic Notes in Discrete Mathematics, Vol. 53, 2016, pp. 287-296.
K.Kayathri and R.Amutha, Enumeration of Edge-Graceful labelings of K3, K4, K5, Mathematical Sciences International Research Journal, Volume 5, Issue 2, ISSN No. 2278-8697, ISBN No. 978-93-84124-93-9, 2016, pp. 21-26.
K.Kayathri and J.Shakila Jemima, EMT labelings and SEMT labelings of connected unicyclic (p,q) graphs with magic constant p+q+3 and 3p, Mathematical Sciences International Research Journal, Volume 5, Issue 2, ISSN No. 2278-8697, ISBN No. 978-93-84124-93-9, 2016, 51-54.
K.Kayathri and G.Kokilambal, Antipodal Domination in terms of the order of graphs, Mathematical Sciences International Research Journal, Volume 5, Issue 2, ISSN No. 2278-8697, ISBN No. 978-93-84124-93-9, 2016, pp. 27-30.
K.Kayathri and S.Vallirani, (1,2)-Domination in graphs, Springer Verlag Lecture Notes in Computer Science,10398,128-133,2017.
G. Kokilambal and K. Kayathri, Restrained Domination in Trees, International Journal of Applied Engineering Research, Vol.14, No.3, ISSN No. 0973-4562, 2019, 37-43.
K. Kayathri and G. Kokilambal, Restrained domination polynomial in graphs, Journal of Discrete Mathematical Sciences & Cryptography,ISSN 0972-0529 (Print), ISSN 2169-0065 (Online),Vol. 22 (2019), No. 5, pp. 761–775,
DOI : 10.1080/09720529.2019.1681693

## Conference/Workshop Attended

Short Term Course on “Programming in Basic” held on 07.08.1989-08.09.1989 at Madurai Kamaraj University, Madurai.
National Seminar on “Current Trends in Graph Theory and its Applications” held on 21.02.1990-28.02.1990 at Annamalai University, Chidambaram.
Symposium on “Graph Theory and Combinatorics” held on 10.05.1991-19.05.1991 at Centre for Mathematical Sciences, Vazhuthacaud, Kerala.
One day Seminar on “Graph Theory and its Applications” held on 17.10.1993 at Manonmaniam Sundaranar University, Tirunelveli.
Symposium on “Mathematical Methods and Applications” held on 22.12.1993 at IIT, Madras.
Orientation Course held on 03.06.1998-30.06.1998 at Academic Staff College, Pondichery University, Pondichery.
Conference on “Graph Theory and its Applications” held on 14.03.2001-16.03.2001 at Anna University, Chennai.
Refresher Course held on 21.11.2001-11.12.2001 at Manonmaniam Sundaranar University, Tirunelveli.
State level Seminar on “Emerging Career Vistas for Mathematicians” held on 05.02.2002 at Arul Anandar College, Karumathur.
National Seminar on “Recent Developments in Concrete Mathematics” held on 22.03.2002 - 23.03.2002 at E.M. Gopalakrishna Kone Yadava Women`S College, Madurai.
National Conference on “Nonlinear Waves and Diffusion” held on 12.09.2003-13.09.2003at Madurai Kamaraj University, Madurai.
National Workshop on “Recent Advances in Mathematics” held on 22.01.2004-25.01.2004 at Cochin University of Science and Technology, Cochin.
Refresher Course on “Recent Trends in Algebra , Analysis, Topology & Applications” held on 03.02.2004-23.02.2004 at Madurai Kamaraj University, Madurai.
State Level Seminar on “Recent Trends in Graph Theory” held on 05.03.2004 at Madurai Kamaraj University, Madurai.
State Level Seminar on “Graph Theory and its Applications” held on 02.08.2004-03.08.2004 at Lady Doak College, Madurai.
National Conference on “Challenges of Higher Education and Future Direction for Autonomous Colleges” held on 23.09.2004-25.09.2004 at Lady Doak College, Madurai.
Symposium on “Promoting Women Leaders in Management and Enterpreneurship” held on 15.10.2004 at Mother Teresa Women`s University, Kodaikanal.
Group Discussion on “Domination in Discrete Structures and Applications” held on 15.09.2004-24.09.2004 at E.M.G. Yadava Women`S College, Madurai.
National Conference on “Graphs, Combinatorics, Algorithms and Applications” held on 25.09.2004-29.09.2004 at Arulmigu Kalasalingam College Of Engineering, Krishnankoil.
Brainstorming Session On Product Graphs and their Applications held on 21.02.2005-22.02.2005 at Bishop Heber College, Tiruchirappalli.
National Seminar on “The Sprit, Culture and Relevance of Mathematics” held on 27.05.2005 - 28.05.2005 at Saraswathi Narayanan College, Madurai.
National Symposium on “Interdisciplinary Applications of Mathematical Modeling” held on 04.08.2005-06.08.2005 at V.V.V. College for Women, Virudhunagar.
Workshop on “The Use of e-journals” held on 28.09.2005 at Madurai Kamaraj University, Madurai.
Research Oriented Lecture Series(Sponsered by DST, New Delhi) on “Mathematics and Applications to Engineering” held on 12.11.2005 at Fathima College, Madurai.
Research Oriented Lecture Series(Sponsered By DST, New Delhi) on “Mathematics and Applications to Engineering” held on 08.07.2006 at Kalasalingam University, Krishnankoil.
State Level Conference on “Recent Advancements in Graph Theory and its Applications” held on 19.08.2006 at The S.F.R. College for Women, Sivakasi.
Research Oriented Lecture Series(Sponsered By Dst, New Delhi) on “Mathematics and Applications to Engineering” held on 23.12.2006 at Saraswathi Narayanan College, Madurai.
National Symposium on “Curriculam Development at P.G.Level in Mathematics” held on 01.03.2007-02.03.2007 at Madurai Kamaraj University, Madurai.
Research Oriented Lecture Series(Sponsered By DST, New Delhi) on “Mathematics and Applications to Engineering” held on 11.03.2007 at Alagappa University, Karaikudi.
Research Oriented Lecture Series(Sponsered by DST, New Delhi) on “Mathematics and Applications to Engineering” held on 04.08.2007 at Saraswathi Narayanan College, Madurai.
National Symposium on “Mathematical Methods and Applications” held on 22.12.2007 at IIT, Madras.
National Symposium on “Graph Theory and its Applications” held on 23.01.2008 at Vivekananda College, Madurai.
International Conference on “Discrete Mathematics” held on 02.06.2008-05.06.2008 at University of Mysore, Mysore.
National Conference on “Recent Trends in Applicable Mathematics for Engineering and Technology” held on 02.04.2009-03.04.2009 at K.L.N. College Of Engineering, Pottapalayam.
Platinum Jubilee 75th Annual Conference of Indian Mathematical Society held on 27.12.2009-30.12.2009 at Kalasalingam University, Krishnankoil.
International Workshop on “Graph Coloring and its Applications” held on 07.08.2010-09.08.2010 at Bharathidasan University, Tiruchirappalli.
Research Oriented Lecture Series(Sponsered By DST, New Delhi) on “Discrete Mathematics and Theoretical Computer Science” held on 29.01.2011at Kalasalingam University, Krishnankoil.
Workshop on “Item Writing Prescribed for College Level” held on 24.03.2011-26.03.2011at Thiagarajar College, Madurai.
Seventh Annual Conference of Academy of Discrete Mathematics and Applications(ADMA) and Graph Theory Day VII held on 09.06.2011-11.06.2011 at National Institute of Technology, Calicut.
“Secrets of Effective Communications” held on 09.07.2011 at Topkids Centre, Madurai.
Research Oriented Lecture Series(Sponsered By Dst, New Delhi) on “Discrete Mathematics and Theoretical Computer Science” held on 24.09.2011at Kalasalingam University, Krishnankoil.
Workshop on “Capacity Building Of Women Managers in Higher Education” held on 26.03.2012-30.03.2012 at Madurai Institute Of Social Sciences, Madurai.
International Workshop on “Combinatorial Algorithms” held on 19.07.2012-21.07.2012 at Kalasalingam University, Krishnankoil.
International Workshop on “Graph Labelings” held on 03.06.2014-06.12.2014 at Kalasalingam University, Krishnankoil.
State Level Workshop on “LaTeX” held on 07.03.2015 at S.B.K. College, Aruppukottai.
National Conference on “Recent Developments on Emerging Fields in Pure and Applied Mathematics” held on 12.03.2015-13.03.2015 at Thiagarajar College, Madurai.
ADMA Pre-Conference Workshop on “Fuzzy Graphs” held on 07.06.2015-09.06.2015 at B.S. Abdur Rahman University, Chennai.
Science Academics Lecture Workshop on “Mathematical Modeling” held on 10.02.2017 and 11.02.2017 at The Madura College, Madurai.
Workshop on “Intellectual Property Rights and Innovation” held on 14.03.2017 at Thiagarajar College, Madurai.
ADMA Pre-Conference school on “Graph Algorithms” held on 05.06.2017-07.06.2017 at SSN College of Engineering, Kalavakam, Chennai.
13th Annual ADMA Conference and Graph Theory Day – XIII held on 08.06.2017 – 10.06.2017 at SSN College of Engineering, Kalavakam, Chennai.
International Conference on “Discrete Mathematics” held on 04.01.2018 – 07.01.2018 at Periyar University, Salem.
International Conference on “Emerging Trends in Graph Theory” held on 27.02.2019 – 28.02.2019 at CHRIST(Deemed to be University), Bangalore.

## Books Published

Two chapters published in the book "Semigraphs and their Applications", 2019, published by Academy of Discrete Mathematics and Applications, India, ISBN: 978-81-940039-0-8

## Lectures

Lectures delivered:

“Edge-chromatic Critical Graphs” in the UGC sponsored State Level Seminar on Graph Theory and its Applications on 3.8.2004 at Lady Doak College, Madurai.
“Fuzzy Graphs” in the UGC sponsored State level seminar on 27.02.2008 at V.V.V. College for Women,Virudhunagar.
“Vertex strength of Fuzzy Graphs” in the UGC sponsored State level seminar on 30.01.2009-31.01.2009 at Sri S.Ramasamy Naidu Memorial College, Sattur.
“Dynamic programming” in the UGC sponsored State level seminar on 19.03.2009 at Mannar thirumalai naicker college, Madurai 5.
“Edge Complete Semigraphs” in the National level –Sixth Annual Instructional Conference of ADMA and Graph Theory Day-VI on 04.06.2010-10.06.2010 at College of Engineering, Pune.
“Applications of Graceful Labelling” in the District level (Virudhunagar District Cluster of Colleges -Joint Faculty Programme) on 31.07.2010 at The S.F.R. College for Women, Sivakasi.
“Edge complete Semigraphs” and “Graceful Labeling” in the UGC-SAP(DRS-I) Programme on 28.03.2011 at Manonmaniam Sundaranar University, Tirunelveli.
“Edge Coloring of Graphs” in the DST sponsored Research oriented Lecture series in Discrete Mathematics and Theoretical Computer Science on 01.10.2011 at National Centre for Advanced Research in Discrete Mathematics, Kalasalingam University.
“Edge coloring of graphs” in the National Level – Eigth Annual Conference of ADMA and Graph Theory Day VIII on 08.06.2012 – 10.06.2012 at V.V.V. College for Women, Virudhunagar.
“Probabilistic Method in Graph Theory” and “Edge completes Semigraphs” in the UGC sponsored Refresher course on 18.02.2013 at Madurai Kamaraj University, Madurai.
“Complete Semigraphs” and “Edge complete Semigraphs” in the National Level - Tenth Annual Conference of ADMA on 10.06.2014-13.06.2014, at Reva institute of technology and management.
“Complete Semigraphs” in the RMS & ADMA sponsored Two Day Workshop on Graph Theory and its Applications on 27.11.2014-28.11.2014 at The Madura College, Madurai
“Semigraphs” in the National Level – Eleventh Annual Conference of ADMA and Graph Theory Day-XI on 10.06.2015-12.06.2015 at B.S. Abdur Rahman University, Chennai 14.
“Edge- chromatic Critical Graphs” in the UGC, DST & CSIR sponsored National Conference on Discrete Mathematics and its Applications on 15.07.2015-17.07.2015 at Manonmaniam Sundaranar University, Tirunelveli
“Semigraphs” in the Research Oriented Lecture on 20.02.2016 at Kalasalingam University, Krishnankovil.
“Enumeration of Labeled Graphs” in the Virudhunagar District Cluster Colleges Meeting on 05.08.2017 at V. V. Vanniaperumal college for women, Virdhunagar.
“Introduction to Fuzzy Algebra” in the Special Lecture on 18.01.2017 at Madurai Sivakasi Nadars Pioneer Meenakshi Womens’s College, Poovanthi.
“Enumeration of Labeled Graphs”in the IX National Conference on Emerging Trends in Graph Theory on10.03.2018 at CHRIST(Deemed to be University), Bengaluru.
“Edge Complete(p,3) Semigraphs” in the National level workshop on Semigraphs and Generalized structure and Dr. V. Swaminathan Endowment Delibrations on 30.10.2018 – 02.11.2018 at V. V. Vanniaperumal college for women, Virdhunagar.
“Complete Semigraphs” in the National level workshop on Semigraphs and Generalized structure and Dr. V. Swaminathan Endowment Delibrations on 30.10.2018 – 02.11.2018 at V. V. Vanniaperumal college for women, Virdhunagar.
“Edge Coloring of Graphs” in the International Conference on Discrete Mathematics on 07.01.2019 – 09.01.2019 at St. Joseph’s College, Tiruchirappalli.
Presentation
“Edge-chromatic critical graphs of order 12” in National seminar on 11.09.1992-12.09.1992 at Madurai Kamaraj University, Madurai.
“On the size of edge-chromatic critical graphs” in National seminar on 05.01.1993-07.01.1993 at Annamalai University.
“A weaker conjecture of Vizing on the size of edge chromatic critical graphs” in International conference on 03.01.1996-06.01.2016 at Ramanujan Mathematical Society.
“Edge complete Semigraphs” in International conference on 15.12.2006-18.12.2006 at Indian Institute of Science, Bangalore.
“Critical graphs with (G)=n and (G)= (G)+1” in International conference on 15.12.2006-18.12.2006 at Indian Institute of Science, Bangalore.
“Edge- chromatic 14- critical graphs” in International conference on 15.12.2006-18.12.2006 at Indian Institute of Science, Bangalore.
“Critical graphs” in International conference on 01.03.2007-03.03.2007 at Loyola college, Chennai.
“Edge complete Semigraphs” in International conference on 01.03.2007-03.03.2007 at Loyola college, Chennai.
“Edge complete (p,3) Semigraphs” in National conference on 31.03.2007 at Saraswathi Narayanan college, Madurai.
“1.Edge chromatic 19-critical graphs” and “2.Edge complete Semigraphs” in International conference on 10.06.2007-14.06.2007 at Kalasalingam University, Krishnankovil.
“Necessary conditions for graceful tree” in International conference on 05.02.2010-06.02.2010 at Loyola college, Chennai.
“Necessary condition for graceful labeling of connected graphs” in International conference on 12.08.2010-15.08.2010 at Cochin University of Science and Technology, Cochin.