FRANCIS RAJ S Associate Professor

Profile Picture

  • Department of Mathematics
  • Ramanujan School of Mathematical Sciences
  • francisraj_s@yahoo.com

Academic Activity

Academic Activity Picture1

Academic Activity Picture2

Educational Qualification (UG,PG & Higher Order)

S.No Degree Subject/Title of thesis University/Board Year of Passing
1 Ph.D. Coloring and Distances in Graphs SASTRA University, Thanjavur 2009
2 M. Phil Mathematics St. Joseph's College, Bharathidasan University, Tr 2005
3 M.Sc. Mathematics St. Joseph's College, Bharathidasan University, Tr 2003
4 B.Sc. Mathematics St. Joseph's College, Bharathidasan University, Tr 2001

Area of Specializaion

Graph Theory

Awards / Prizes Conferred

S.No Name / Title of the Award Type Name of the Agency conferred the Award Year of the Award Amount for Cash Award
1 IMS prize for the year 2009 for presenting the best research paper in the area of Discrete Mathematics NATIONAL Indian Mathematical Society 2009 nil

Teaching Experience

S.No Designation Department/Centre Institution
1 Assistant Professor Mathematics Pondicherry University

Research Experience

S.No Designation Department/Centre Institution Area of Research
1 Post Doctoral Fellow Mathematics Bharathidasan University Graph Theory
2 Senior Research Fellow Mathematics SASTRA University Graph Theory
3 Junior Research Fellow Mathematics SASTRA University Graph Theory

Industry Experience

S.No Designation Company/Corporate Nature of Work

Contribution towards Innovation

S.No Name of the Work/Contribution Specialization Remarks

Patent Details

S.No Title Status Patent Number Year of Award Type Commercialized Status

Papers Published in UGC Approved Journals

S.No Title Name of the Authors as per the order in Paper Journal Name Volume, Issue & Page Nos. Year Impact Factor

Papers Published in Non UGC Approved Peer Reviewed Journals

S.No Title Name of the Authors as per the order in Paper Journal Name Volume, Issue & Page Nos. Year Impact Factor
1 On indicated coloring of lexicographic product of graphs P. Francis, S. Francis Raj and M. Gokulnath Discrete Applied Mathematics Available online from 2021. https: //doi.org /10.1016 /j.dam. 2021. 04.021 2021 1.139
2 Indicated coloring of Cartesian product of some families of graphs P. Francis, S. Francis Raj and M. Gokulnath Ars Combinatoria 154, 143–157 2021 0.258
3 b-coloring of the Mycielskian of some classes of graphs S. Francis Raj and M. Gokulnath Discussiones Mathematicae Graph Theory available online https://doi.org/10.7151/dmgt.2265 2019 0.714
4 Indicated coloring of some classes of graphs P. Francis, S. Francis Raj and M. Gokulnath Graphs and Combinatorics 35, 1105–1127 2019 0.498
5 b-coloring of Cartesian product of odd graphs R. Balakrishnan, S. Francis Raj and T. Kavaskar Ars Combinatoria 131, 285-298 2017 0.258
6 On b-coloring of powers of Hypercubes P. Francis and S. Francis Raj Discrete Applied Mathematics 225, 74-86 2017 1.139
7 On two Conjectures on b-coloring of graph products S. Francis Raj and T. Kavaskar Studia Scientiarum Mathematicarum Hungarica 54 (1) 141–149 2017 0.301
8 On Indicated Chromatic number of graphs S. Francis Raj, R. Pandiya Raj, H.P.Patil Graphs and Combinatorics 33, 203–219 2017 0.498
9 b-coloring of Cartesian Product of trees R. Balakrishnan, S. Francis Raj and T. Kavaskar Taiwanese Journal of Mathematics 20, 1–11 2016 1.136
10 Bounds for the b-chromatic number of subgraphs and edge-deleted subgraphs P. Francis and S. Francis Raj Discussiones Mathematicae Graph Theory 36, 959–976 2016 0.714
11 On Indicated Coloring of Graphs R. Pandiya Raj, S. Francis Raj, H. P. Patil Graphs and Combinatorics 31, 2357–2367 2015 0.498
12 Bounds for the b-chromatic number of the Mycielskian of some families of graphs R. Balakrishnan and S. Francis Raj Ars Combinatoria 122, 89- 96 2015 0.258
13 Bounds for the b-chromatic number of Cartesian product of graphs R. Balakrishnan, S. Francis Raj and T. Kavaskar Graphs and Combinatorics 30, 511-520 2014 0.498
14 Connectivity of the Generalised Mycielskian of Digraphs S. Francis Raj Graphs and Combinatorics 29 893–900 2013 0.498
15 Bounds for the b-chromatic number of G-v R. Balakrishnan and S. Francis Raj Discrete Applied Mathematics 161 (9) 1173-1179 2013 1.139
16 The Wiener number of powers of the Mycielskian R. Balakrishnan and S. Francis Raj Discussiones Mathematicae Graph Theory 30 (3) 489- 498 2010 0.714
17 The Wiener number of Kneser Graphs R. Balakrishnan and S. Francis Raj Discussiones Mathematicae Graph Theory 28 (2) 219-228 2008 0.714
18 Connectivity of the Mycielskain of a graph R. Balakrishnan and S. Francis Raj Discrete Mathematics 308 (18) 2607 – 2610 2008 0,87

Papers Published in Conference Proceedings

S.No Title Name of the Authors as per the order in Paper Details of Conference Publication Page Nos. Year
1 b-Coloring of Some Powers of Hypercubes P. Francis, S. Francis Raj and M. Gokulnath CALDAM 2021, Lecture notes in Computer Science LNCS, 12601 282-287 2021
2 Indicated Coloring of Complete Expansion and Lexicograp hic Product of Graphs P. Francis, S. Francis Raj and M. Gokulnath CALDAM 2020, Lecture notes in Computer Science LNCS, 12016 178-183 2020
3 b-coloring of the Mycielskian of regular graphs S. Francis Raj, M. Gokulnath CALDAM 2019, Lecture notes in Computer Science LNCS, 11394 91-96 2019
4 On Indicated Coloring of some classes of graphs P. Francis, S. Francis Raj, M. Gokulnath CALDAM 2018, Lecture notes in Computer Science LNCS, 10743 73-80 2018
5 Indicated coloring of Cartesian product of graphs P. Francis and S. Francis Raj ICTCSDM 2017, Lecture notes in Computer Science LNCS 10398 63-68 2017
6 The b-chromatic number of powers of Hypercube P. Francis, S. Francis Raj Electronic Notes in Discrete Mathematics 53 , 459–464 2016
7 Bounds for the b-chromatic Number of Induced Subgraphs and G − e P. Francis and S. Francis Raj CALDAM 2015, Lecture notes in Computer Science LNCS, 8959 147-152 2015
8 Super connectivity of the generalised Mycielskian of graphs Francis Raj S IWOCA, Lecture notes in Computer Science LNCS, 7643 122-124 2012

Books

S.No Title of the Book Name of the Authors as per the order in Book Publisher Year ISBN No.

Chapters in Books

S.No Title of the Chapters Name of the Authors Title of the Book Publisher Year ISBN No.

Edited Books

S.No Title of the Book Name of the Authors as per the order in Book Publisher Year ISBN No.

Ongoing Projects

S.No Title of the Project Sponsored By Period Sanctioned Amount(Rs. Lakh) Year
1 SomeProblemsonb-coloringand Indicated Coloring of Graphs Department of Science and Technology 3 years 14,45,180 2017

Ongoing Consultancy Works

S.No Title of the Consultancy Work Sponsored By Period Sanctioned Amount(Rs. Lakh) Year

Completed Projects

S.No Title of the Project Sponsored By Period Sanctioned Amount(Rs. Lakh) Year

Completed Consultancy Works

S.No Title of the Consultancy Work Sponsored By Period Sanctioned Amount(Rs. Lakh) Year

Career Guidance Offered to students

S.No Name of the Scheme No. of Students Competitive Examinations/ Career Counseling No. of Students Passed No. of Students Placed

List of capability enhancement such as Soft skill development, Remedial coaching, Language lab,
Bridge courses, Yoga, Meditation, Personal Counselling and Mentoring etc.,

S.No Name of the Programme/Scheme Date of Implementation No. of Students Enrolled Agencies Involved

Research Guidance - PG

S.No Year Degree No. of Students Awarded Department/Centre

Research Guidance - Ph.D

S.No Student Name Registration Date Registration No. Thesis Title Thesis Submitted Status Thesis Submitted Date Vivavoce Completed Status Date Awarded
1 M. Gokulnath 24-08-2015 20151118005 b-coloring and indicated coloring of graphs YES 22-02-2021 YES 27-09-2021
2 Francis. P 24-08-2012 PHD 1313 A study on b-coloring and indicated coloring of graph YES 12-02-2018 YES 29-08-2018

Research Guidance - Post Doctoral

S.No Scholar Name Designation Funding Agency Fellowship Title Year of Joining Year of Completion

Financial assistance availed to attend conferences / workshops and to pay membership fee
of professional bodies during the year

S.No Conference/ workshop attended for which financial support provided Professional body for which membership fee is provided Amount of Support Place From Date To Date Year
1 Third India Taiwan Conference on Discrete Mathematics No memberhip fee 43000 (approx.) National Chiao Tung University, Hsinchu, Taiwan 19-11-2013 22-11-2013 2013

E-Lecture Details

S.No E-Lecture Title Development of e-content/e-learning/delivering Member of Editorial Bodies Reviewer/Referee of
Content/Module Title Institution/Platform Year Weblink

Details of Online Education Conducted

S.No Nature of Online Course No. of Sessions Target Group Date

Invited Talks in Conference/Seminar/Workshop/Training Programme

S.No Title of the Paper Conferences/Seminar/Workshop/Training Programme Organized by Whether International / National / State / Regional / College or University Level From To Year
1 On Chi-binding function for {F, F^c}-free graphs International Conference on Theoretical and Computational Graph Theory Vellalar College for Women and VET Institute of Arts and Science College, Erode International 10-01-2024 12-01-2024 2024
2 Indicated Coloring of Lexicographic Product of Graphs International Conference on Graph Theory Periyar University, Salem International 08-01-2024 09-01-2024 2024
3 Interpolation Theorem for some Colouring Parameters International Conference on Recent Trends in Applied Graph Theory ICRTAGT 2023 Sree Kerelavarma College, Thrissur International 01-02-2023 01-02-2023 2023
4 Problem Solving in Analysis Three day Workshop on Problem Solving in Analyss, Algebra and Differential Equations (PAAD 2023) St. Joseph's College, Trichy State 25-09-2023 27-09-2023 2023
5 Graph Coloring Master's Colloquium in association with International Conference on Recent advances in Graph Theory and Allied Areas ICRAGAA 2023 St. Aloysius College, Thrissur State 04-02-2023 04-02-2023 2023
6 Chromatic Bounds for some Superclasses of 2K_2-free Graphs International Conference on Recent advances in Graph Theory and Allied Areas ICRAGAA 2023 St. Aloysius College, Thrissur International 02-02-2023 04-02-2023 2023
7 Graph Coloring Problems BOMAC Club Cauvery College, Trichy College 17-08-2022 17-08-2022 2022
8 Graph Theory as a tool in Mathematics MATHFORUM SASTRA Deemed University, Kumbakonam College 07-11-2022 07-11-2022 2022
9 A Combinatorial Proof of Brouwer's fixed point theorem National Seminar on Number Theory and Combinatorics Central University of Tamil Nadu, Thiruvarur, Tamil Nadu National 19-12-2022 19-12-2022 2022
10 Combinatorics in Pure Mathematics Mathematics Association Inaugural St. Joseph's College, Trichy College 17-08-2022 17-08-2022 2022
11 Chi-binding function for pK_2-free graphs 37th Annual Conference of Ramanujan Mathematical Society Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam National 06-12-2022 08-12-2022 2022
12 On a special type of game coloring of graphs 23rd Ramanujan Symposium- National Conference on Graph Theory and its Application University of Madras, Chennai National 04-03-2020 06-03-2020 2020
13 Coloring game of graphs National Webinar D.G. Vaishna v College, Chennai National 19-09-2020 19-09-2020 2020
14 Interpolation Theorems in Graph Coloring 6th India-Taiwan Conference on Discrete Mathematics 2019 IIT (BHU), Varanasi International 15-11-2019 18-11-2019 2019
15 Real Analysis and its Applications National Seminar on Mathematical Analysis and its Applications SDNB Vaishnav College for Women, Chennai National 09-10-2019 09-10-2019 2019
16 b-coloring of the Mycielskian of some Graphs International Conference on Discrete Mathematics 2019 St. Joseph’s College, Trichy International 07-01-2019 09-01-2019 2019
17 Connectivity & Super-connectivity of the Generalised Mycielskian of graphs International Conference on Recent trends in Graph Theory and Combinatorics CUSAT, Cochin International 26-04-2018 29-04-2018 2018
18 Bounds for the b-chromatic number of Subgraphs and extremal graphs International Conference on Discrete Mathematics Periyar University, Salem International 04-01-2018 07-01-2018 2018
19 Interpolation Theorems in Graph Coloring 14th Annual ADMA Conference and Graph Theory Day 2018 DAIICT, IIT Gandhinagar, IIIT Vadodara National 06-06-2018 10-06-2018 2018
20 Graph Colouring National Seminar on Graph Theory Holy cross College, Nagercoil National 23-10-2017 23-10-2017 2017
21 On Indicated Coloring of Graphs The Fifth India- Taiwan Conference on Discrete Mathematics Department of Mathematics, Tamkang University International 18-07-2017 21-07-2017 2017
22 Coloring Games in Graphs National Conference on Advanced Trends in Mathematics Thiruvalluvar University College of Arts and Science, Vandavasi National 27-03-2017 27-03-2017 2017
23 A brief survey on Indicated coloring of graphs Two Day National Seminar on some recent research directions in Graph Theory Ayya Nadar Janaki Ammal College, Sivakasi National 09-03-2017 10-03-2017 2017
24 On b-coloring of Graph Products National Worshop on Product Graphs Periyar University, Salem National 23-02-2017 25-02-2017 2017
25 On b-coloring of powers of hypercubes International Conference on Theoretical Computer Science and Discrete Mathematics Kalasalingam University, Krishnankoil, Tamil Nadu. International 19-12-2016 21-12-2016 2016
26 Graph Coloring problems National Conference on Contemporary Graph Theory and its Applications Sermathai Vasan College for Women, Madurai National 11-01-2016 11-01-2016 2016
27 Interpolation type results for indicated coloring of graphs National Conference on Discrete Mathematics St. Joseph’s College, Trichy National 09-01-2015 10-01-2015 2015
28 b-continuity of graphs National Seminar on Emerging trends in Graph Theory St. Aloysius’ College, Kerala National 21-01-2015 23-01-2015 2015
29 On b-coloring and b-continuity of graphs Three day National Conference on recent developments in Coloring, Domination and Distinguishing codes in graphs Government Arts College, Melur, Tamil Nadu National 06-08-2015 08-08-2015 2015
30 Interpolation type results for indicated coloring of graphs Fourth India-Taiwan Conference on Discrete Mathematics IIT Madras, Chennai. International 10-07-2015 13-07-2015 2015
31 On b-coloring of powers of hypercubes International Conference on Graph Theory and its Applications Amrita University, Coimbatore International 16-12-2015 19-12-2015 2015
32 On Game Coloring of Graphs One day National Conference on Recent Advances in Computer and Mathematical Sciences De. Umayal Ramanathan College for Women National 17-10-2014 17-10-2014 2014
33 On Indicated coloring of graphs International Conference on Algebra and Discrete Mathematcis Government College, Kattappana, Kerala International 04-03-2014 06-03-2014 2014
34 b-coloring of regular graphs National Workshop on graph coloring (NWGC 2013) Indian Statical Institute Chennai centre, Chennai National 25-01-2013 27-01-2013 2013
35 Graph Theoretic Applications in Engineering Faculty development programme Government College of engineering, Bargur State 07-02-2013 13-02-2013 2013
36 Mycielski Construction International Conference on Discrete Mathematics ICDM 2013 Karnatak University, Dharwad International 10-06-2013 14-06-2013 2013
37 b-continuity of graphs National Conference on Graph Coloring and its Applications Dr. Ambedkar Institute of Technology, Bangalore National 27-06-2013 28-06-2013 2013
38 b-coloring and b-continuity of graphs State level seminar on New Trends in Graph Theory Ayya Nadar Janaki Ammal College, Sivakasi State 13-09-2013 13-09-2013 2013
39 b-chromatic number of product graphs Third Indo-Taiwan Conference in Discrete Mathematics National Chiao Tung University, Hsinshu Taiwan International 19-09-2013 22-09-2013 2013
40 On Mycielskian graphs National Conference on Graph Theory and its Applications P.K.R. Arts College for Women, Gobichettipalayam National 22-08-2013 22-08-2013 2013
41 On b-coloring of regular graphs National Seminar on Recent trends in coloring of graphs and digraphs Sethupathy government arts college, Ramanathapuram National 24-08-2012 25-08-2012 2012
42 Some Problems on graph coloring National Seminar on Discrete Mathematics and its Applications Periyar Maniammai University, Thanjavur National 27-07-2012 27-07-2012 2012
43 On the b-chromatic number of graph products National Workshop on Decomposition of graphs and Product graphs Periyar University, Salem National 22-06-2011 25-06-2011 2011
44 b-coloring of Cartesian Product of graphs International Workshop on Graph Coloring and its Applications Bharathidasan University International 07-08-2010 09-08-2010 2010
45 A note on the Mycielski construction Sixth Annual Instructional conference of ADMA and Graph Theory Day VI Department of Mathematics, College of Engineering, Pune National 04-06-2010 07-06-2010 2010
46 b-coloring of graphs First Indo-Taiwan Conference in Discrete Mathematics National Taiwan University, Taipei International 09-11-2009 11-11-2009 2009

Conferences/Seminars Organized

S.No Title of the Programme Sponsors Venue & Duration Whether International / National / State / Regional / College or University Level From To Year
1 International Conference on Graph Theory and its applications DST & Pondicherry Univerity Department of Mathematics, Pondicherry University, Puducherry & 2 days International 15-07-2015 16-07-2015 2015

Workshop Organized

S.No Title of the Programme Sponsors Venue & Duration Whether International / National / State / Regional / College or University Level From To Year
1 National Workshop on Graph Coloring and Algebraic Graph Theory UGC-SAP DRS II Department of Mathematics & 5 days National 06-03-2018 10-03-2018 2018
2 Workshop on recent trends in Graph Theory and its Applications UGC-SAP DRS I Department of Mathematics, Pondicherry University, Puducherry & 3 days National 07-02-2011 09-02-2011 2011

Administrative Responsibilities in the Government and Quasi Government Agencies

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Affiliation in Academic Bodies/Societies

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Participation & Extension Activities (Academic/Administraion)

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Participation & Extension Activities (Co-Curricular)

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Collaboration with Institution/Industry

S.No Collaborator Name Designation Institution/Industry Type Nature of Collaboration Period of Collaboration Visits to Collaborating
Institution / Industry		 Details of Collaborative Research/Teaching
From Date To Date From Date To Date

Faculty Development Programme Attended (Orientation, Refresher, other Short Term Course during the year)

S.No Title of the FDP Organiser Venue Duration From Date To Date Year

Details of Executive Development Prog/Management Development Prog. conducted

S.No Name of the Programme No. of Participants Venue Duration From Date To Date Year Revenue Generated

Participation in IMPESS, IMPRINT, SPARC, STARS, LEAP Programme etc and DSF Funding Programme

S.No IMPRESS/IMPRINT/SPARC/STARS/LEAP/Others Place From Date To Date Year

Enrolment under ARPIT Programme

S.No Name of the Programme Period of the Programme
From Date To Date