@nss.org.in

Assistant Professor in Mathematics

N S S College, Kerala University

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

rkkmaths@

rkkresearch@

PROFESSIONAL RESEARCH EXPERIENCE

• 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

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

Collaborators

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

Applications Invited

Collaborators

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

Collaborators

18

Scopus Publications

575

Scholar Citations

7

Scholar h-index

3

Scholar i10-index

- 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. - Developing an Efficient Waste Management System: An Approach by Using Some Methods of Mathematical Modelling

K Reji Kumar and E N Satheesh

IOP Publishing - 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

IEEE

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

IEEE

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

IEEE

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

IEEE

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

IEEE

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

- E-WASTE: A FURIOUSLY GROWING TECHNICAL WASTE WITH MINIMUM MANAGEMENT PERSPECTIVES IN INDIA

S KHATAK, H SINGH, R KUMAR

2025 - 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 - BUDGETING OF BIOMASS AND CARBON STOCK AS ECOSYSTEM SERVICE FROM HIMALAYAN DRY TEMPERATE AND ALPINE FOREST ECOSYSTEM, INDIA.

R KUMAR, DR BHARDWAJ, RP YADAV, V NEGI

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 - RECALLING IMMUNE RESPONSES POST VISCERAL LEISHMANIASIS

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

2022 - High-speed interconnects: History, evolution, and the road ahead

BK Kaushik, R Sharma, PP Paltani, VR Kumbhare, R Kumar, S Kumar, ...

2022 - Coupled diffusion-mechanics framework for simulating hydrogen assisted deformation and failure behavior of metals

DK Mahajan, R Kumar, V Singh, Y Charles

2022 - 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 - PP349 [Medical Workforce & Education Staff education]: CRITICAL CARE HEALTH WORKERS KNOWLEDGE OF ALARM FATIGUE AND PRACTICES TOWARDS ALARMS AT THE KENYATTA NATIONAL HOSPITAL

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

EUROPEAN JOURNAL OF NUCLEAR MEDICINE AND MOLECULAR IMAGING 49 (SUPPL 1 2022 - 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, ...

EUROPEAN JOURNAL OF NUCLEAR MEDICINE AND MOLECULAR IMAGING 49 (SUPPL 1 2022

- 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