Assistant Professor in Mathematics
N S S College, Kerala University


K. Reji Kumar, Ph. D.
Assistant Professor and the Head of the Department
P. G. Department of Mathematics
N. S. S. College, Cherthala
Kochuramapuram (P.O.) Alappuzha
PIN: 689 501


• Awarded summer research fellowship of Indian Academy of Sciences and did post-doctoral
research in Indian Statistical Institute, at the Delhi center for two months (1st April 2007 to 30th May 2007), under the supervision of Prof. R. B. Bapat.
• Did post-doctoral research in Dept. of Mathematics and Statistics, University of
Victoria, Canada, from 1st April 2008 to 1st November 2008. I got the BOYSCAST fellowship of the Department of Science and Technology, India.


MSc (Mathematics), MA (Philosophy), B. Ed,
M. Phil (Applied Mathematics), Ph. D (Mathematics)


Graph Theory, Discrete Mathematics, Mathematical Modeling, Consciousness Research


Mathematical Modeling of Consciousness

The aim of the project is to develop a mathematical theory of Human Consciousness. An axiomatic approach to the study of consciousness is already under consideration. According to this theory, models form the basic units of consciousness. There are three types of models

Applications Invited

Domination in Graph Theory and Related Topics

Domination is an established area of research in Graph Theory. The project aims at further research in this area.

Applications Invited

Mathematics for Social Change and Development

Mathematics is not a subject just for study and teaching. It has the fascinating potential of applications in all fields of knowledge. This project aims at exploring all such possibilities.

Applications Invited

Scopus Publications


Scholar Citations


Scholar h-index


Scholar i10-index

Scopus Publications

  • A Comparative Study of Kerala School of Mathematics with European School: Based on Network Analysis
    K. Reji Kumar, C. M. Indukala, and E. N. Satheesh

    Springer Singapore

  • Safe Eternal m - Secure sets in Graphs
    K. Reji Kumar and E.N. Satheesh

    IOP Publishing
    Abstract An eternal 1-secure set, in a graph G = (V, E) is a set D ⊂ V having the property that for any finite sequence of vertices r 1, r 2,…,rk , there exists a sequence of vertices v 1,v 2,…,vk and a sequence D = D 0, D 1, D 2,…, Dk of dominating sets of G, such that for each i, 1 ⩾ i ⩾ k, Di = (D i-1 − {vi }) ∪ {ri }, where vi ∈ D i−1, and ri ∈ N[vi ], where ri = vi is possible. The cardinality of a smallest eternal 1 - secure set in a graph G is called the eternal 1 - security number of G. This situation can be interpreted as defending an attack at the place ri by moving a guard from vi to ri , where guards are deployed at the places, which are represented by the vertices in D i−1. An eternal m - secure set is defined in a similar way with only one exception that in response to an attack more than one guards can move to its adjacent locations to defend an attack. A vertex is safe eternal m - secure if it is either adjacent to exactly one vertex in an eternal m - secure set or present in the set itself. In this paper we study some properties of safe eternal m - secure sets. Safe eternal m - security number (σsm ) is the minimum cardinality of all safe eternal m - secure sets in a graph. We also find the safe eternal m - security number of some classes of graphs.

  • An Approximation to m-Ranking Method in Networks
    K. Reji Kumar and Shibu Manuel

    Springer International Publishing
    Identifying important nodes in a network is an important area of research in network science. m-ranking method is a method proposed Reji Kumar et al. [18] for ranking the nodes in a network which avoids the chance of assigning same rank for two nodes with different physical characteristics. This ranking takes into account the degree of all nodes and weights of all edges in a network. As the network becomes bigger and bigger the m-ranking method takes more and more time to complete. To overcome this difficulty in this paper we propose an approximation to this method, which simplifies the calculations without undermining the ranking outcome. We illustrate the procedure in some example networks.

  • A Network Analysis of the Contributions of Kerala in the Field of Mathematical Research Over the Last Three Decades
    K. Reji Kumar and Shibu Manuel

    Springer International Publishing
    In this paper we compare the performance made by higher educational institutions in Kerala (a southern state in India) in the field Mathematical research for the period from 1981 to 2015. The entire period is conveniently divided into periods of five years. We use some techniques from social network analysis to compare the performance of institutions over time. His study is based on the research papers published by the faculty of the institutions in the national and international journals which are indexed and listed by MatScinet of American Mathematical Society, which is a prominent abstracting agency in the field of Mathematics. Data available in the data base of MatScinet is used to prepare the network of collaborations of the institutions. These networks are further analyzed and compared to arrive at many valuable conclusions.

  • Collaborations of Indian institutions which conduct mathematical research: A study from the perspective of social network analysis
    K. Reji Kumar and Shibu Manuel

    Springer Science and Business Media LLC
    Expansion of knowledge in the realm of higher mathematics is highly important when progress of human society is concerned. As a fast developing country, in India we need a monitoring system which would tell us the exact nature of changes taking place in the field of mathematics. This is the motivation behind this paper. In this paper we present an analysis of the network formed by institutions which conduct research and publish articles in the field of Mathematics. Collaboration between a member of one institute and a member of another institute make a connection between the institutions. We make a comparative study of the network formed in consecutive years over a period of time giving emphasis to importance of institutions in the research network.

  • Interior exterior and boundary of fuzzy soft multi topology in decision making
    K. Reji Kumar and S. A. Naisal

    In this paper we define some properties of soft multi sets. We also define soft multi set topology, its interior, exterior, boundary and their properties. We discuss mathematical modeling of spacial objects using fuzzy soft interior, fuzzy soft exterior, fuzzy soft boundary. A decision making problem is also included. Main aim of this study is to give an extension of the existing studies of special objects and to give better result using fuzzy soft set theory. An application of fuzzy concepts and the topological interior, exterior, and boundary is clearly available [11] in the literature. Here we find the maximum affected area of Mikania micrantha using interior, boundary and exterior by taking row maximum and row minimum using the numerical value of resultant fuzzy soft sets. It also provides conceptual definition and explanation along with a quantitative description of topological aspects between spacial objects.

  • The m-Ranking of nodes in complex networks
    K. Reji Kumar, Shibu Manuel, and Deepu Benson

    Identifying influential nodes in complex networks has attracted much attention because of its great theoretical significance and wide application. The m-Ranking method takes into account degree of all nodes and weight of all edges to rank nodes of the network with different weight. This ranking method can be used for unweighted networks also by fixing the value of the parameter α = 1. In addition, we demonstrate our new method on a real air traffic network and show that the ranks calculated using the new method is more meaningful compared with other methods.

  • Spreading information in complex networks: A modified method
    Rejikumar Karunakaran and Shibu Manuel

    Spreading information in complex networks is studied by researchers using methods such as k — shell decomposition, degree k, closeness centrality etc. In this paper we discuss the importance of increase in degree of vertiees in a network in spreading information. We also pinpoint some important flaws in the existing methods and propose a modified method to do the identification of the most influential nodes as spreaders.

  • Mathematical modeling of consciousness: A foundation for information processing
    Rejikumar Karunakaran

    Human consciousness is modeled mathematically, using models as fundamental units [6]. It is hypothesized that consciousness is the effect of all model based activities taking place in our mind. In this paper we initiate a study to explain how the complex phenomenon of consciousness evolves from a very simple, fundamental level.

  • Mathematical modeling of consciousness: Subjectivity of mind
    K. Reji Kumar

    In this article, our research focuses on the subjectivity of human experiences. We discuss the possible reasons for subjectivity and present a mathematical model which explains this phenomenon. Also an objective way to measure the subjectivity of human thinking is introduced.

  • Efficient domination in circulant graphs
    K. Reji Kumar and Gary MacGillivray

    Elsevier BV
    Abstract Results about wreath products of circulant graphs are used to construct infinitely many circulant graphs with efficient dominating sets whose elements need not be equally spaced in Z n . It is proved that if a circulant graph of large degree has an efficient dominating set, then either its elements are equally spaced, or the graph is the wreath product of a smaller circulant graph with an efficient dominating set and a complete graph.

  • Topological properties of the set of all minimal total dominating functions of a graph

  • Structure of the set of all minimal total dominating functions of some classes of graphs
    K.Reji Kumar and Gary MacGillivray

    Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora
    In this paper we study some of the structural properties of the set of all minimal total dominating functions (FT ) of cycles and paths and introduce the idea of function reducible graphs and function separable graphs. It is proved that a function reducible graph is a function separable graph. We shall also see how the idea of function reducibility is used to study the structure of FT (G) for some classes of graphs.

  • On the ideal convergence of sequences of fuzzy numbers
    Vijay Kumar and Kuldeep Kumar

    Elsevier BV
    In this paper we introduce and study the concepts of I-convergence, I^*-convergence and I-Cauchy sequence for sequences of fuzzy numbers where I denotes the ideal of subsets of N, the set of positive integers.

  • Basic minimal dominating functions

  • On maximal fractional independent sets in graphs



  • Earthworm Castings in Ecosystem Health through Their Elemental Composition
    P Baskar, K Sachan, BV Singh, DRK Saikanth, RKM Kumar, R Gautam, ...
    International Journal of Plant & Soil Science 35 (18), 2076-2087 2023

    Applied Ecology & Environmental Research 21 (4) 2023

  • Comparative Performance of Indigenous Uttara Chicken with Three Well-Established Breeds under Rural Farming
    P PATEL, S KUMAR, AK Ghosh, B SINGH, R Kumar, R VERMA, ...
    Indian Journal of Animal Production and Management 37 (2), 164-171 2023

    B Singh, S Chauhan, A Shukla, V Verma, R Kumar, S Sundar
    International Journal of Infectious Diseases 130, S24 2023

  • Understanding the low-energy incomplete fusion reactions
    A Yadav, G Ram, MS Asnain, I Majeed, M Shuaib, VR Sharma, I Bala, ...
    Physical Review C 107 (4), 044605 2023

  • Synthesis of silver nanoparticles by green method using ligustrum sinense to study their structural and photoluminescence properties
    SA Khan, S Patel, P Shukla, R Kumar, R Dixit
    Eurasian Journal of Physics and Functional Materials 7 (1), 52-59 2023

  • The female microbiome profile in patients undergoing bladder instillation therapy for treatment of bladder pain syndrome
    EK Welch, R Kumar, P Mathanraj, J Kugelman, C Pekny, KL Dengler, ...
    American Journal of Obstetrics & Gynecology 228 (3), S828 2023

  • Practical single-fibre network-oriented quantum key distribution from a compact source of entangled photons in presence of White Rabbit time synchronisation
    KP Schatz, B Amies-King, S Albosh, R Kumar, M Lucamarini
    Quantum Technology: Driving Commercialisation of an Enabling Science III 2023

  • Phase noise characterisation of a 2-km hollow-core nested antiresonant nodeless fibre for twin-field quantum key distribution
    M Minder, S Albosh, O Alia, R Slavik, R Kumar, F Poletti, G Kanellos, ...
    Quantum Technology: Driving Commercialisation of an Enabling Science III 2023

  • Decomposing the linear momentum transfer components in break-up fusion reactions: An experimental study of the system
    MS Asnain, M Shuaib, I Majeed, MK Sharma, A Yadav, DP Singh, ...
    Physical Review C 106 (6), 064607 2022

  • Towards the development of a task oriented robotic assistance in vertical farming
    A Dogra, R Kumar, E Singla

  • High-speed interconnects: History, evolution, and the road ahead
    BK Kaushik, R Sharma, PP Paltani, VR Kumbhare, R Kumar, S Kumar, ...

  • Coupled diffusion-mechanics framework for simulating hydrogen assisted deformation and failure behavior of metals
    DK Mahajan, R Kumar, V Singh, Y Charles

  • 214P Versican G3 domain promotes myeloma cell proliferation, migration and invasion via activation of FAK/STAT3 signaling
    N Gupta, R Kumar, A Sharma
    Annals of Oncology 33, S1518 2022

    LC Kimeto, B Reel, R Kumar, O Yanay
    Pediatric Critical Care Medicine 23 (Supplement 1 11S) 2022

  • Study of incomplete fusion reaction dynamics for the system 14N+ 169Tm using the forward Recoil Range distribution technique
    S Kumar, PK Giri, R Kumar, A Yadav, R Ali, S Appannababu, A Agarwal, ...
    Journal of Physics G: Nuclear and Particle Physics 49 (10), 105103 2022

  • Design, Synthesis, and biological evaluation of quinoline based Sigma-2 receptor-specific 99mTc-(DTPA) Isoquinoline complex for SPECT Imaging of breast tumor
    V Chaudhary, S Chaturvedi, A Anju, R Kumar, AK Mishra

  • Phase 2 study evaluating safety, PK/PD, biomarkers, and efficacy of ANX005 in patients with Huntington's disease (HD)
    R Kumar, D Claassen, A Mongan, A Grover, B Hoehn, P Lin, R Arnold, ...
    MOVEMENT DISORDERS 37, S300-S301 2022

  • (131) Iodine scan image denoising using deep neural network
    A Pandey, J Chaudhary, A Hemrom, PD Sharma, C Patel, CS Bal, ...


  • Efficient Domination in Circulant Graphs
    GMG K. Reji Kumar
    Discrete Mathematics 313, 767–771 2013
    Citations: 37

  • An improved k-shell decomposition for complex networks based on potential edge weights
    S Manuel, KR Kumar
    Int. J of Applied Mathematical Sciences, 163-168 2016
    Citations: 13

  • Fractional independence and fractional domination chain in graphs
    S Arumugam, K Rejikumar
    AKCE International Journal of Graphs and Combinatorics 4 (2), 161-169 2007
    Citations: 11

  • Spectrum of (k, r)-regular hypergraphs
    KR Kumar, RP Varghese
    International Journal of Mathematical Combinatorics 2, 52 2017
    Citations: 9

  • Spreading information in complex networks: A modified method
    K Reji Kumar, S Manuel
    Proceedings of International Conference on Emerging Technological Trends 2016
    Citations: 9

  • Spectra of a new join of two graphs
    RP Varghese, KR Kumar
    Advances in Theoretical and Applied Mathematics 11 (4), 459-470 2016
    Citations: 8

  • Modeling of consciousness: classification of models
    KR Kumar
    Advanced Studies in Biology 3, 141-146 2010
    Citations: 8

  • Mathematical modeling of consciousness: Subjectivity of mind
    KR Kumar
    2016 International Conference on Circuit, Power and Computing Technologies 2016
    Citations: 7

  • Intrusion detection system for manet using machine learning and state transition analysis
    TS Bharati, R Kumar, SN Tadiboina
    Int J Comput Eng Technol 6 (12), 1-8 2015
    Citations: 7

  • A comparative study of the SIR prediction models and disease control strategies: a case study of the State of Kerala, India
    K Reji Kumar
    Computational Intelligence Methods in COVID-19: Surveillance, Prevention 2021
    Citations: 6

  • The m-ranking of nodes in complex networks
    KR Kumar, S Manuel, D Benson
    2017 9th International Conference on Communication Systems and Networks 2017
    Citations: 6

  • Basic minimal dominating functions
    KR Kumar, S Arumugam
    Utilitas Mathematica 77, 235 2008
    Citations: 6

  • Collaborations of Indian institutions which conduct mathematical research: A study from the perspective of social network analysis
    K Reji Kumar, S Manuel
    Scientometrics 117 (2), 1041-1051 2018
    Citations: 5

  • Field Evaluation of Fungitoxicants for the Control of Leaf Spot of Sunflower (Altemaria alternata (Fr.) Keissler)
    R Kumar, SB Singh
    ADVANCES IN PLANT SCIENCES 10, 233-236 1997
    Citations: 5

  • Geochemistry and Phase equilibrium modelling of garnet-biotite gneiss from Mauranipur, Bundelkhand Craton, Northern India; implication for tectonic setting and metamorphism
    P Pathak, SB Dwivedi, RR Kumar
    Journal of Geosciences Research. Under Review 2022
    Citations: 4

  • Nipah outbreak in Kerala–A network-based study
    KR Kumar
    Journal of Physics: Conference Series 1850 (1), 012019 2021
    Citations: 4

  • Efficacy of neural network in rainfall-Runoff modelling of Bagmati River Basin
    K Kumar, V Singh, T Roshni
    International Journal of Civil Engineering and Technology (IJCIET) 9 (11), 37-46 2018
    Citations: 4

  • Indian business
    P Budhwar, R Kumar, A Varma
    Routledge 2017
    Citations: 4

  • Personal influence on the spreading of information: A network based study
    KR Kumar, S Manuel
    International Journal of Mathematics Trends and Technology-IJMTT 52 2017
    Citations: 4

  • How does consciousness overcome combinatorial complexity?
    R Kumar
    Artificial Intelligence and Evolutionary Algorithms in Engineering Systems 2015
    Citations: 4