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Department has been recognized as a Research Center by Visvesvarayya Technological University (VTU) in the year 2006 to offer PhD programs.

Eligibility Criteria for enrolment to Ph.D is as per VTU norms (www.vtu.ac.in).

Research Areas: Spectral Graph Theory, Graph Polynomials, Graph Energy, Distances in Graphs, Semi-graphs, Signed graphs, Wiener Index, Derived graphs, Laplacian polynomial, Chromatic polynomial, Differential Geometry, Fluid Dynamics, Numerical Methods, Complex Analysis. 

Conference/Seminar/Workshop Organized:

  1. “Workshop on Scilab”, July 20-21, 2016.
  2. “Workshop on Latex”, March 3-4, 2016.
  3. “National Seminar on Recent Advances in Mathematics and Its Applications” Jan 28-29, 2014.
  4. “Two Days Workshop on Differential equations and Geometry”, May 15-16 2014.
  5. “Symposium on Graph Theory”,Nov 21, 2012
Sl.No Name Research Area Research Students Email ID
1  Dr. P. R. Hampiholi  Spectral Graph Theory 4 prhampiholi@git.edu
2  Dr. S. R. Jog  Graph Polynomial 3 sudhir@git.edu
Research Scholars Registered for Ph.D. at Mathematics Department, Research Centre GIT

Sl.No. Research Scholar Research Guide Registration Date Present Status
1  Mr. D. S. Revankar  Dr. H. S. Ramane May 2006 Ph.D Awarded
2  Mr. B. S. Durgi  Dr. P. R. Hampiholi May 2007  Ph.D Awarded
3  Mr. S. P. Hande  Dr. S. R. Jog May  2008 Ph.D Awarded
4  Ms. A. B. Ganagi  Dr. H. S. Ramane  May 2010 Ph.D Awarded
5  Ms. S. M. Gudimani  Dr. H. S. Ramane  May 2010  Thesis Submitted
6  Ms. S. S. Shinde  Dr. H. S. Ramane May 2010  Thesis Submitted
7  Mr. Jotiba Kiturkar  Dr. P. R. Hampiholi  Nov 2010  Comprehensive Viva Completed
8  Mrs. Meenal Kaliwal  Dr. P. R. Hampiholi  Nov 2010  Comprehensive Viva Completed
9  Ms. J. B. Patil  Dr. H. S. Ramane Dec 2011  Comprehensive Viva Completed
10  Mr. Raju Kotambari  Dr. S. R. Jog  Dec 2013  Comprehensive Viva Completed
11  Mr. Shrinath L. Patil  Dr. S. R. Jog  Dec 2013  Registered
 12 Mrs. A. S. Joshi Dr. P. R. Hampiholi  Dec 2015  Registered
13 Mr. J. R. Gurjar Dr. S. R. Jog Dec 2015 Registered

  Research Scholars Registered for Ph.D. at Research Centre other than GIT

Sl.No. Research Scholar Research Guide Registration Date Present Status
1 Mr. B. J. Jirage  Dr. V. B. Awati  April 2016  Course Work Completed
 2 Mrs. P. S. Hande  Dr. D. S. Revankar  Dec 2015  Registered
 3 Mr. B. B. Digewadi Dr.  S. N. Bansode  April 2013   Course Work Completed
         
Computer, Laptop and research library.
Research Projects

VTU Grant Research Project at Mathematics Research Center, GIT for the duration 2008-2011.

Title of the Grant: Distance Eigenvalues of Graphs

Principal Investigator: Dr. H. S. Ramane Co-Investigator: Dr. P. R. Hampiholi, Dr. S. R. Jog

Amount of grant sanctioned: Rs. 1,00,000/-

Total no. of Journal papers from Recognition of research center

National Journal: 2

1)”Acoustic measurements of flow due to reverse dune structure bed form”, Mr. B. J. Jirage, Proc. of National    Conference on Applied Mathematics, K.L.E. Society’s Gudleppa Hallikeri College, Haveri Jan 30-31 2015, ISBN: 978-81-930850-2-8.

2)”On upper bounds for energy of bipartite graphs”, B. Zhou, H. S. Ramane, Indian J. Pure and Applied Mathematics, 39(6), (December 2008), 483 – 490. ISSN: 0019-5588, Impact Factor: 0.294.

International Journal: 45

1)”Alternative Energy Options for India- A Multi-criteria Decision Analysis fot Rank Energy Alternatives using
    Analytic Hierarchy Process and Fuzzy Logic with an Emphasis to Distributed Generation”, Mr. S. H. Kulkarni,
    Mr. B. J. Jirage, Dr. T. R. Anil, Distributed Generation and Alternative Energy Journal, Vol. 32, No. 2, 2017, ISSN:  
    2156-3306.
2)”Similarity Solutions of the MHD Boundary Layer Flow Past a Constant Wedge within Porous Media”,RB
    Kudenatti, SR Kirsur, AL Nargund, NM Bujurke – Mathematical Problems in Engineering, Volume 2017 (2017),
    Article ID 1428137, 11 pages
3)”The -projective curvature tensor field on Generalized -Paracontact Metric Manifold”, D. G.  Prakasha, L. M.
     Fernandez and K. K.Mirji, To be appearing in Georg. Math. J. (2017) (Accepted)
4)”On Enumeration of Some Semigraphs”, Dr. P. R. Hampiholi, J. Kitturkar
5)”Performance Evalution of a 800 kW Wind Power Project and Analysis of Factors Affecting Wind Power
    Generation”, Mr. S. H. Kulkarni, Mr. B. J. Jirage, Dr. T. R. Anil, Mechanical Engineering, Elixir Mech. Engg.    
     94(2016)   4011-40117 ISSN: 2229-712x.
6)”Hamming distance between the strings generated by adjacency matrix of a graph and their sum”, Algebra and
    Discrete Mathematics Vol. 22 (2016). Number 1, pp. 82- 93.
7)”On the adjacency , Laplacian and sign less Laplacian energy of coalsecnce of complete graphs”, Journal of
     Mathematics, Hindwai Publishers, July 2016.
8)”On the -projective curvature tensor of a -contact metric manifold”, D. G. Prakasha and K. K. Mirji, Facta
     Universitatis (NIS): Ser. Math. Inform. Vol. 32, No 1 (2017), 117–128.
9)”On the pseudo-quasi-conformal curvature tensor of sasakian manifolds”, D. G. Prakasha, T. R. Shivamurthy and
      K. K. Mirji, Electronic Journal of Mathematical Analysis and Applications, Vol. 5(2) July 2017, pp. 147-155.
10)”On -projectivelysymmetric Kenmotsu manifolds”, D. G. Prakasha, Ngaraja M. and K. K. Mirji, New Trends in
        Mathematics, Vol. 4, 295-305 (2016).
11)”Degree sum energy of some graphs”,  S. R. Jog, Raju Kotambari. Annulus of Pure and Applied Mathematics  2016
        vol.1, No. 11, ISSN: 2016 2279-087X
12) “Minimum Covering Energy Of Some Thorny Graphs”. S. R. Jog, Raju Kotambari. Asian Journal Of Mathematics
       and Applications, Volume 2014, Article ID ama0171.
13)“Zagreb Co indices on some operationas on Tadpole Graph”. D.S. Revankar, S.P. Hande, S.R. Jog, P. S. Hande,
       M. M. Patil. Int Journal of Computer and mathematical sciences, ISSN: 2347-8527, Vol:3(9),Nov 2014.
14)“Bounds for the degree sum eigenvalue and degree sum energy of a common neighborhood graph”. S. P.Hande,
      Dr. S.R. Jog and D. S. Revankar. International journal of graph theory, Volume 1(4), August 2013.
 15)“Derived graph of sub division graph”.S.P.Hande, S.R.Jog, H.S.Ramane, P.R.Hampiholi, I. Gutman, and B.S,Durgi.
      Kragujevac Journal of Mathematics (Serbia),Vol37 (2),2013,319-32.
16)“Degree sum polynomial of graph valued function on Regular Graphs”.S.R.Jog ,S. P. Hande, D.S.Revankar.
       International journal of graph theory, Vol.1(3), June-2013,ISSN:2320-6543 ,130-138.
17)“Hamming index of class of graphs”. H. S. Ramane, A. B. Ganagi. International Journal of current engineering &
      technology, 2013.
18)“Wiener Index of a Graph in terms of eccentricities”. H. S. Ramane, A. B. Ganagi,H. B. Walikar. Iranian Journal of
      Mathematical Chemistry,2013.
19)”Energy of complement of stars”, P.R.Hampiholi, H.B.Walikar, B.S.Durgi., Indones. Math. Soc., Vol. 19,
       No. 1(2013), pp 15 – 21.
20) “On the spectra and  energy of some cluster graphs”, P.R.Hampiholi, B.S.Durgi., International J. of Math. Sci. &
       Engg. Appls. (IJMSEA).  Vol. 7, No. II (2013), 219-228.
21) “On the energy of complement of stars”, P.R.Hampiholi, B.S.Durgi, H.B.Walikar., International J. of Math. Sci. &
       Engg. Appls. (IJMSEA). Vol. 7, No. II, (2013).139-148.
22)”Characteristic polynomial of some cluster graphs”, P.R.Hampiholi, B.S.Durgi., Kragujevac Journal of
      Mathematics.. Vol. 2 No. II, (2013)
23)”Almost minimal graphs by interlacing eigenvalues by divisor technique”, P.R.Hampiholi, B.S.Durgi., International
      Journal of Graph Theory,Vol.1, Issue 2, (2013),80 – 91.
24)”Spectra of some class of graphs using interlacing”, P.R.Hampiholi, B.S.Durgi., International Journal of Graph
      Theory, Vol. 1, 3(2013),
25)”Partial Edge Incidence Matrix of Semigraph over GF(Over 22)”, P.R.Hampihokli, J.Kitturkar, International
       Journal  of Engineering Research & Technology Vol. 3 Issue 9, September- 2014 ,1213 – 1216
26)”Distance Spectra and Energy of some cluster graphs”, B.S.Durgi,P.R.Hampiholi,S.M.Mekkalki, Mathematica
      Aeterna,vol.4, Issue 8,Dec 2014.
27)”Bounds for the signless Laplacian eigenvalues of graphs”, H. S. Ramane, S. S. Shinde, S. B. Gudimani, J. B. Patil, 
      International Journal of Mathematical Sciences and Engineering Applications, 6(VI)(2012), 129 – 135. ISSN:  
      0973-9424
28)”Overlap based results on absolute sum coefficients of chromatic polynomials”, Dr. S. R. Jog, S. P. Hande,
     International Journal of Mathematical Sciences and Engineering Applications, 6(VI)(2012), 137 – 143. ISSN: 
     0973-9424.
29)”Derived graphs of some graphs”, S. R. Jog, S. P. Hande, I. Gutman, S. B. Bozkurt, Kragujevac Journal of
      Mathematics, 36(2)(2012), 309 – 314. ISSN: 1450-9628, Impact Factor: 0.275.
30)”On a conjecture on the diameter of line graphs of graphs of diameter two”, H. S. Ramane, A. B. Ganagi, I.
       Gutman, Kragujevac Journal of Mathematics, 36(1) (2012),  59 – 62. ISSN: 1450-9628, Impact Factor: 0.275.
31)”On the Wiener index of a graph”, H. S. Ramane, D. S. Revankar, A. B. Ganagi,  Journal of Indonesian
       Mathematical Society, 18(1)(2012), 57 – 66. ISSN: 0854-1380.
32)”On some new polynomial and its eigenvalues”, S. R. Jog, S. P. Hande, International Journal of Mathematics and
      Computer Applications Research, 2(1)(2012), 91 – 99. ISSN: 2249-6955 (Print), 2249-8060 (Online), Impact
      Factor: 0.9754.
33)”Wiener index of trees whose edge independence number is four”, H. S. Ramane, D. S. Revankar, A. B. Ganagi, 
     International Journal of Mathematics and Computer Applications Research, 1(2)(2011), 50 – 68. ISSN:
      2249-6955 (Print), 2249-8060 (Online), Impact Factor: 0.9754.
34)”Counterexamples for properties of line graphs of graphs of diameter two”, H. S. Ramane, I. Gutman, Kragujevac
       Journal of Mathematics, 34(2010), 147 – 150. ISSN: 1450-9628, Impact Factor: 0.275.
35)“Distance spectra and Distance energies of iterated line graphs of regular graphs”, H.. S. Ramane, D. S. Revankar,
       I. Gutman, H. B. Walikar,  Publications de L’Institut Mathematique, 85(99) (2009), 39 – 46. ISSN: 0350-1302.
36)”Equienergetic graphs”, H.S. Ramane, H. B. Walikar and I. Gutman, The Journal of Combinatorial Mathematics
      and Combinatorial Computing, 69(2009), 165 – 173. ISSN: 0835-3026.
37)“Distance Equienergetic Graphs”, H. S. Ramane, I. Gutman, D. S. Revankar,  MATCH Commun. Math. Comput.
       Chem., 60 (2008), 473 – 484. (Serbia). ISSN: 1450-9628, Impact Factor: 3.5.
38)“On an open problem of R. Balakrishnan and the energy of the product of graphs”, H. B. Walikar, H. S. Ramane,
       S. R. Jog,  Graph Theory Notes, New York, 55 (2008), 41 – 44. ISSN: 1040-8118.
39)“Estimating the distance energy of graphs”, H. S. Ramane, D. S. Revankar, I. Gutman, S. B. Rao, B. D. Acharya,
       H. B. Walikar,  Graph Theory Notes, New York, 55 (2008), 27 – 32. ISSN: 1040-8118.
40)“Bounds for the distance energy of a graph”, H. S. Ramane, D. S. Revankar, I. Gutman, S. B. Rao, B. D. Acharya,
      H. B. Walikar, Kargujevac J. Math., 31 (2008), 59 – 68. ISSN: 1450-9628, Impact Factor: 0.275.
41)“Laplacian polynomial and number of spanning trees in terms of characteristic polynomial of induced subgraphs”,
      H. B. Walikar and H. S. Ramane,  AKCE International Journal of Graphs and Combinatorics, 5(1) (2008), 47 –
      55. (India).
42)“Partially balanced incomplete block designs arising from minimal dominating sets of a graph”, H. B. Walikar,
      B. D. Acharya, H. S. Ramane, H. G. Shekharappa, S. Arumugam, AKCE International Journal of Graphs and
      Combinatorics, 4(2)(2007), 223 – 232.
43)“On equienergetic graphs and molecular graphs”, H. B. Walikar, H. S. Ramane, Kargujevac J. Sci., 29 (2007),
      73 – 84. (Serbia). ISSN: 1450-9636, Impact Factor: 0.622.
44)“Construction of equienergetic graphs”, H. S. Ramane, H. B. Walikar, MATCH Commun. Math. Comput. Chem.,
       57 (2007), 203 – 210. (Serbia & Montengro). ISSN: 1450-9628, Impact Factor: 3.5.
45)“Hosoya polynomial of thorn trees, rods, rings and stars”, H. B. Walikar, H. S. Ramane, L. R. Sindagi, S. S. Shirkol  
       and I. Gutman, Kargujevac J. Sci., 28 (2006), 47 – 56. (Serbia). ISSN: 1450-9636, Impact Factor: 0.622.

Total no. of Conference papers from Recognition of research center

National Conference: 20

1)”Study on solution of Elastohydrodynamic Problem Using Multigrid Method”, Mr. Bhairu J. Jirage, National Conference on Analysis and its Applications, organized by Dept. of Mathematics Karnatak University, Dharwad during 15th & 16th March, 2017.

2)”The conharmonic curvature tensor on-Paracontact Metric Manifolds”, Dr. K. K. Mirji, National Conference on Analysis and its Applications, organized by Dept. of Mathematics Karnatak University, Dharwad during 15th & 16th March, 2017.

3)”On Maximum Degree Energy of Some Graphs”, Dr. S. R. Jog, ADMA, S. I. T, Tumakuru, June 9-11, 2016.

4)”Acoustic measurements of flow due to reverse dune structure bed form”, Mr. Bhairu J. Jirage, UGC sponsored National Conference Applied Mathematics, Gudleppa Hallikeri College, Haveri, Karnataka, 2015 January, 30-31st.

5)“Energy of Institionistic Fuzzy Graphs”, Bhairu J. Jirage, 10th Annual Conference of ADMA & Graph Theory Day,Reva Institute of Technology & Management, 2014 June, 10th-13th.

6)”Spectra of Mysceleskin of some graphs”, Dr. S. R. Jog, 10th Annual Conference of ADMA & Graph Theory Day,Reva Institute of Technology & Management, 2014 June, 10th-13th.

7)”Uniqueness Related to Multiple values & Derivatives on Annuli”, Dr. S. R. Kabbur, National conference on Engineering Applications of Mathematics, MIT Academy of Engineering, Pune, Maharastra. 2014, June 5 & 6.

8)“Spectra of graphs”, B. S. Durgi, P. R. Hampiholi, Symposium on Advances in Graph Theory, Gogte institute of Technology, Belgaum, 21st Nov. 2012.

9)“Bounds on the signless Laplacian eigenvalues”, S. S. Shinde, H. S. Ramane, Symposium on Advances in Graph Theory, Gogte institute of Technology, Belgaum, 21st Nov. 2012.

10)“Signless Laplacian polynomial and characteristic polynomial of a graph”, S. B. Gudimani, H. S. Ramane, Symposium on Advances in Graph Theory, Gogte institute of Technology, Belgaum, 21st Nov. 2012.

11)“Derived graphs”, S. P. Hande, S. R. Jog, Symposium on Advances in Graph Theory, Gogte institute of Technology, Belgaum, 21st Nov. 2012.

12)“Properties of semigraph”, M. Kaliwal, P. R. Hampiholi, Symposium on Advances in Graph Theory, Gogte institute of Technology, Belgaum, 21st Nov. 2012.

13)“Matrix of semigraph”, J. P. Kitturkar, P. R. Hampiholi, Symposium on Advances in Graph Theory, Gogte institute of Technology, Belgaum, 21st Nov. 2012.

14)“Distance equienergetic graphs”, D. S. Revankar, H. S. Ramane, Symposium on Advances in Graph Theory, Gogte institute of Technology, Belgaum, 21st Nov. 2012.

15)“On absolute sum of chromatic coefficients”, S. P. Hande Eight Annual Conference of Academy of Discrete Mathematics and Applications (ADMA), V. V. V. College for Women, Virudhunagar, June 8 – 10, 2012.

16)“On some new polynomial and eigenvalues”, S. R. Jog, Eight Annual Conference of Academy of Discrete Mathematics and Applications (ADMA), V. V. V. College for Women, Virudhunagar, June 8 – 10, 2012.

17)“Distance spectra and distance energies of graphs”,  H. S. Ramane, National Conference on Algorithms, Computing, Graph Theory and Combinatorics, Visvesvaraya Technological University, Belgaum, April 20 – 22, 2011.

18)“On the Wiener number of trees whose edge independence number is four”, Miss A.B. Ganagi, National Conference on Distance in Graphs, Poornaprajna College Udupi, Oct 4-6, 2010.

19) “Distance energy of a graph” , H. S. Ramane, D. S. Revankar, Sixth Annual Conference of ADMA and Graph Theory Day VI, College of Engineering, Pune, June 8 – 10, 2010.

20) “Generating  Hyperenergetic Cluster graphs”,  P. R. Hampiholi, S. R. Jog,  National Conference on Mathematical Methods and Applications, B.E.C. Bagalkot, March 17-18, 2007.

International Conference: 14

1)”Laplacian and Signless Laplacian Energy of Thorn Graphs”, Dr. S. R. Jog, International Conference on Discrete & Computational Mathematics-2017, The Ganchigram Rural Institute-Deemed Univeristy, Gandhigram, Tamilnadu, Feb 16-18 2017.

2)”Effect of Variable Porosity on Boundary Layer Flow”, Mr. B. J. Jirage, International Conference on Mathematics, Physics & Allied Sciences, Carmel College, Goa, Mar 03-05,2016.

3)“Spectra of Myselskia of some graphs”, Dr. S. R. Jog, “International Conference On Advances in Mathematical Sciences and Applications” at Adichunchanagiri Institute of Technology, Chikmagalur, Karnataka, 2014 December, 22-23.

4)“Study on Magnetic Fluid Based Squeeze Film between Truncated Conical Plates” Mr. Bhairu J. Jirage, “International Conference On Advances in Mathematical Sciences and Applications” at Adichunchanagiri Institute of Technology, Chikmagalur, Karnataka, 2014 December, 22-23.

5)”Minimum Covering energy of some graphs”, Dr. S. R. Jog, “International Conference On Advances in Mathematical Sciences and Applications” at Adichunchanagiri Institute of Technology, Chikmagalur, Karnataka, 2014 December, 22-23.

6) “On the Uniqueness of Meromorphic functions that Share a Set (IM) on Annuli”,Dr.S.R.Kabbur, “International Conference On Advances in Mathematical Sciences and Applications” at Adichunchanagiri Institute of Technology, Chikmagalur, Karnataka, 2014 December, 22-23.

7)“Experimental Study of Turbulent Nature of Fluid Flow Under Sediment”, Bhairu J. Jirage, International Conference on Emerging Trends in Mathematical Sciences at Vijanagar Sri Krishnadevaraya University, Bellary. 2014 July, 25-26.

8)“Energy of complement of star graphs”, P. R. Hampiholi, B. S. Durgi, H. B. Walikar, 5th International Conference on Research and Education in Mathematics (ICREM5), Institute Technology Bandung, Indonesia, Oct. 22 – 24, 2011.

9)“On the Wiener index of a graph”, H. S. Ramane, D. S. Revankar, A. B. Ganagi,  5th International Conference on Research and Education in Mathematics (ICREM5), Institute Technology Bandung, Indonesia, Oct. 22 – 24, 2011.

10)“Distance spectra and distance energy of a iterated line graph of a regular graph”,  H. S. Ramane, D. S. Revankar, I. Gutman, H. B. Walikar, International Conference on Recent Trends in Graph Theory and Combinatorics, Cochin University of Science and Technology, Cochin, Aug. 12 – 15, 2010.

11)“Estimating the distance enrgy of graphs”, H. S. Ramane, D. S. Revankar,  International Conference on Discrete Mathematics, Mysore University, Mysore, June 6 – 10, 2008.

12)“On the open problem of R. Balakrishnan and energy of some products of graphs”, S. R. Jog, S. P. Hande,  International Conference on Discrete Mathematics, Mysore University, Mysore, June 6 – 10, 2008.

13) “Generation of equienergetic graphs”, H. S. Ramane, H. B. Walikar, S. B. Halkarni, International Conference on Discrete Mathematics, Indian Institute of Science, Bangalore, Dec. 15 – 18, 2006.

14)“Bounds for the eigenvalues of distance polynomial of a graph”,  H. S. Ramane, D. S. Revankar, International Conference on Discrete Mathematics, Indian Institute of Science, Bangalore, Dec. 15 – 18, 2006.