**Dr. Ranjini. P. S **is currently holding the position of Professor in the Department of Mathematics, Don Bosco Institute of Technology and is flourished with a Teaching Experience of 16 Years and 9 Years of Research Experience. She conferred Ph. D in Mathematics in the year 2011 from Visvesvaraya Technological University, Belgaum. She has done her M. Sc from University of Calicut in the year 2000 and M.Phil from Madurai KamaRaj University in the year 2003.
**Academic and Co-curricular Responsibilities :**

She is having passion towards her Profession and is engaged in Research activities, Mentoring, Students Progressive Monitoring system and other Department related activities.
**Courses Handled : **

She is an Expert in the various areas like Graph Theory, Engineering Mathematics, Linear Algebra, Functional analysis, Operation Research, Calculus of Variation, Differential Equation etc.
**Additional Responsibilities as per NAAC or NBA : **She is actively involved in all the Departmental activities.
**Paper Publications & Presentations :**

• Ranjini. P. S, V. Lokesha and M. A. Rajan, On Zagreb Indices of the Subdivision Graphs, Int. J. Math. Sc. Eng. App. Vol.4 (3) (2010), pp. 221- 228. ISSN: 0973 9424. http://www.ascent.Journals.com

• Ranjini. P. S, V. Lokesha and M. A. Rajan , On the Zagreb Indices of the Line Graphs of the Subdivision Graphs, Applied Mathematics and Computation, (2011), U SA, ISSN: 0096-3009. http://www.elseveier.com/locate/amc

• Ranjini. P. S and V. Lokesha, The Smarandache-Zagreb Indices on the Three Graph Operators, Int. J. Math. Combin, Vol. 3(2010), China, pp. 1-10. ISSN: 1937 - 1055

• Ranjini. P. S and V. Lokesha , The Wiener Polynomial for the Subdivision Graphs (1), Chinese Journal of Engineering and Mathematics, Vol. 28(3), June (2011), pp. 1–8.

• M. A. Rajan , Ranjini. P. S and V. Lokesha, On New Vertex Naturally Labeled Graphs, Int. e-Journal of Mathematics and Engineering, Vol.109 (2010), pp. 992–999. ISSN: 0976–1411. www.internationalejournals.com

• M. A. Rajan , Ranjini. P. S and V. Lokesha , Connectivity Index of Some Graph Operations, Int. Journal of Physical Sciences, Vol. 22(3)M, (Sep 2010), pp. 895 – 900. ISSN: 0970 – 9150.

• Ranjini. P. S and V. Lokesha , On the Bounds of the Largest Eigen Value and the Laplacian Energy of Certain Class of Graphs, Scientia Magna, Vol. 6(4), (2010), China, pp.15- 19 ISSN:1556 -6706. http://wwwlib.Umi.com/bod/

• Ranjini. P. S and V. Lokesha , On the Szeged Index and the PI Index of the Subdivision Graph of Certain Class of Graphs, Bulletin of Pure and Applied Mathematics, Vol.6(1),(2012)pp. 9 - 24. ISSN: 0973- 5933.

• Ranjini. P. S, V. Lokesha and K. A . Germina, Eigen Values and Energy of Group Graphs, J. Intelligent System Research, Vol.1 (2), pp. 105 - 109, (2007). ISSN: 0973 - 4856. www.serials publications.com/Journal.asp

• Ranjini. P. S and V. Lokesha , On Zagreb indices of the subdivision Graphs, J. Orissa Math. Soc. Vol.30(1),(2011), pp. 71 -79.

• Ranjini. P. S and V. Lokesha , Eccentric Connectivity Index, Hyper and Reverse-Wiener indices of the Subdivision Graph, General Mathematics Notes, Vol. 1(2), (2011),pp. 34 - 46. ISSN: 2219 - 7184. www.i-csrs.org

• Ranjini. P. S and V. Lokesha , On The Shultz Index Of the Subdivision Graphs, Adv. Studies Contemporary. Math, 21(3), (2011), South Korea. pp. 279 – 290, ISSN: 1229 – 3076. http://www.scinagojr.com

• M. A. Rajan, Ranjini. P. S and V. Lokesha , Permanent of a Matrix a Combinatorial Study of Graphs, Proceedings of the Jangjeon Mathematical Society, Vol. 11(1)(2008), pp.97-104.

• M. A. Rajan, Ranjini. P. S and V. Lokesha , A Study on Series Edge Graph Transformation, Proc. 23rd Joint Iran-South Korea Jang Math. Soc. Iran (2010).

• M. A. Rajan, Ranjini. P. S and V. Lokesha , On Some Properties of Splitting Graph of a Graph , Antarctica Journal of Mathematics, Vol. 8(2)(2011), pp.103-108, ISSN: 0972 – 8643.

• A. R. Bindusree, Ranjini. P. S and V. Lokesha , Relation Connecting Zagreb Co-indices on Three Graph Operators,Mathematica Aterna, Vol. 3(6)(2013), pp.433-448, ISSN: 0972 – 8643.

• Ranjini. P. S and V. Lokesha , On Bounds on Szeged and Pi Index in terms of Second Zagreb Index, Int. J. Math. Combin, V.1(2012), PP. 47 – 50, ISSN: 1937 – 1055.

• Princy. K. L, Ranjini. P. S and V. Lokesha, On Square Difference Graphs, Int. J. Math. Combin, Vol.1(2012), PP. 31 – 40, ISSN: 1937 – 1055.

• B. Shwetha Shetty, Ranjini. P. S and V. Lokesha , Computing Some Topological Indices of Smart Polymer, Digest Journal of Nanomaterials and Biostructures, Vol. 7(3),( 2012), pp. 1097 – 1102.

• B. Shwetha Shetty, Ranjini. P. S and V. Lokesha , New bounds for Randic and GA indices, Journal of Inequalities and Applications, V.180(2013), PP.1– 7, ISSN: 1029 – 242X. http://www.springer open.com

• B. Shwetha Shetty, Ranjini. P. S and V. Lokesha , A comparative Study of Topological Indices and Molecular Weight of Some Carbohydrates, Journal of Indian Acad. Math, Vol. 34(2),( 2012), pp. 627 – 636, ISSN: 0970 – 5120.

• A. R. Bindusree, Ranjini. P. S and V. Lokesha New Bounds On Zagreb Indices and Zagreb Coindices, Bol. Soc. Paran. Mat, Vol. 31(1)(2013), pp.51-55, ISSN: 2175 – 1188. www.spm.uem.br/bspm

• Usha. A, Ranjini. P. S and V. Lokesha, Relation between Phenylene and Hexagonal Squeeze Using Harmonic index, International Journal of Graph Theory, Vol. 1(4)(2013), pp.116-121, ISSN: 2320 – 6543.

• B. Shwetha Shetty, Ranjini. P. S , V. Lokesha and Naci Cangul, Computing Some Topological Indices Of Smart Polymer, Digest Journal of Nanomaterials and Biostructures, Vol. 7(3)(2012), pp. 1097 – 1102.

• R. Bindusree, Ranjini. P. S and V. Lokesha , On H- Line Graphs, Advanced Studies in Contemporary Mathematics, 24(3)(2014), pp. 397 - 403

• Usha, Ranjini. P. S and V. Lokesha Trees, Unicyclic Graphs Extremal with respect to Kekule Index, Advanced Studies in Contemporary Mathematics, 24(3)(2014), pp. 301- 308.

• P. S. Ranjini, Trees , Unicyclic Graphs Extremal with respect to Sum Connectivity Index, Proceedings of Jangieon Mathematical Society, 17(3)(2014), pp. 369- 374.

• Ranjini. P. S and V. Lokesha , Sharp Bounds For SZ, PI and GA2 Indices in terms of the Number of Triangles, Ilirias Journal of Mathematics, Volume 4 ( 1) (2015), PP 41-49. ISSN: 2334-6574

• B. Shwetha Shetty , K. C. Gupta, Ranjini. P. S and V. Lokesha Graph Operations On the Symmetric Division Deg Index of Graphs, Palestine Journal of Mathematics, Vol. 6(1)(2017) , pp.280 – 286

• Eccentric Connectivity Index, Hyper and Reverse - Wiener Indices of the Subdivision Graph, UGC Sponsored National Conference on Applications of Mathematics and Statistics, March 25-26, 2011, Yuvaraja's College, Mysore.

• Bounds on Eigen Value and the Laplacian Energy of Certain Class of Graphs, First National Conference on Wireless Control and Communication Technology, April 27-28, 2011, Dr. AIT, Bangalore.

• The Zagreb Indices on Three Graph Operators of Certain Classes of Graphs, DST Sponsored National Conference, Applied and Engineering Mathematics, July 28-30, 2011, RNSIT, Bangalore.

• Trees and Unicyclic Graphs Extremal with Respect to Sum Connectivity Index, Global Advancement of Mathematics, 26th International Conference of Jangjeon Mathematical Society, South Korea, 1st -4 th August 2013, in association with Acharya Institute Of Graduate Studies, Bangalore.

• Invited talk on Various Topological Indices, National Conference on Recent Developments in Mathematics and their Applications (NCRDMA-2014), sponsored by UGC, New Delhi. The conference was organized by Department of Mathematics, University College of Science, Tumkur University in association with Department of Studies and Research in Mathematics, Tumkur University.

• An Investigation of Topological Indices using an Operator on Simple Graphs, National Conference on Recent Developments in Mathematics and their Applications (NCRDMA-2014), sponsored by UGC, New Delhi.

**Research Area :**Her research area is Graph Theory and is engaged in Research activities. She is guiding four students which leads to the Doctoral Degree and one Ph. D Scholar has submitted the Ph. D thesis under her supervision at VTU.
**Achievements : **

• Received the Young Scientist Award in the Year 2013 in the 26th International Conference of Jangeon Mathematical Society, South Korea.

• She is been appreciated by college and awarded the appreciation certification for 100% results in the subjects she teaches.

Address

Don Bosco Group of Institutions,Mysore Road, Kumbalagodu,

Bangalore - 560074, Karnataka, India.

Phones

8880-716-716

Email Addresses