Verified email at yahoo.co.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@yahoo.co.in

rkkresearch@yahoo.co.in

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

16

Scopus Publications

94

Scholar Citations

5

Scholar h-index

2

Scholar i10-index

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

K Reji Kumar and E N Satheesh

IOP Conference Series: Materials Science and Engineering, ISSN: 17578981, eISSN: 1757899X, Volume: 872, Published: 26 June 2020 IOP Publishing - An Approximation to m-Ranking Method in Networks

K. Reji Kumar and Shibu Manuel

Lecture Notes on Data Engineering and Communications Technologies, ISSN: 23674512, eISSN: 23674520, Pages: 344-352, Published: 2020 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

Lecture Notes on Data Engineering and Communications Technologies, ISSN: 23674512, eISSN: 23674520, Pages: 585-590, Published: 2020 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

Scientometrics, ISSN: 01389130, eISSN: 15882861, Volume: 117, Pages: 1041-1051, Published: 1 November 2018 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

2016 International Conference on Control Instrumentation Communication and Computational Technologies, ICCICCT 2016, Pages: 147-152, Published: 21 July 2017 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

2017 9th International Conference on Communication Systems and Networks, COMSNETS 2017, Pages: 413-414, Published: 9 June 2017 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. - Mathematical modeling of consciousness: A foundation for information processing

Rejikumar Karunakaran

Proceedings of IEEE International Conference on Emerging Technological Trends in Computing, Communications and Electrical Engineering, ICETT 2016, Published: 7 March 2017 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. - Spreading information in complex networks: A modified method

Rejikumar Karunakaran and Shibu Manuel

Proceedings of IEEE International Conference on Emerging Technological Trends in Computing, Communications and Electrical Engineering, ICETT 2016, Published: 7 March 2017 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: Subjectivity of mind

K. Reji Kumar

Proceedings of IEEE International Conference on Circuit, Power and Computing Technologies, ICCPCT 2016, Published: 2 August 2016 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. - A mathematical modeling of Ayurveda doshas: Application of fuzzy soft topology

International Journal of Pure and Applied Mathematics, ISSN: 13118080, eISSN: 13143395, Volume: 106, Pages: 33-43, Published: 2016 - Efficient domination in circulant graphs

K. Reji Kumar and Gary MacGillivray

Discrete Mathematics, ISSN: 0012365X, Volume: 313, Pages: 767-771, Published: 2013 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

Journal of Combinatorial Mathematics and Combinatorial Computing, ISSN: 08353026, Pages: 213-223, Published: February 2011 - Structure of the set of all minimal total dominating functions of some classes of graphs

K.Reji Kumar and Gary MacGillivray

Discussiones Mathematicae - Graph Theory, ISSN: 12343099, Pages: 407-423, Published: 2010 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

Information Sciences, ISSN: 00200255, Volume: 178, Pages: 4670-4678, Published: 15 December 2008 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

Utilitas Mathematica, ISSN: 03153681, Pages: 235-247, Published: November 2008 - On maximal fractional independent sets in graphs

Ars Combinatoria, ISSN: 03817032, Pages: 205-212, Published: April 2008

- An Approximation to m-Ranking Method in Networks

KR Kumar, S Manuel

Intelligent Communication Technologies and Virtual Mobile Networks, 344-352 2019 - A Centrality Measure for Directed Networks: m-Ranking Method

R Kumar, S Manuel

Social Networks and Surveillance for Society, 115-128 2019 - A Network Analysis of the Contributions of Kerala in the Field of Mathematical Research Over the Last Three Decades

KR Kumar, S Manuel

International conference on Computer Networks, Big data and IoT, 585-590 2018 - Spectra of a New Join in Duplication Graph

KR Kumar, RP Varghese

Mathematical Combinatorics, 53 2018 - Intuitionistic Fuzzy Soft Multiset and its Application

KR Kumar, SA Naisal

International Journal of Mathematical Combinatorics, 155-163 2018 - Collaborations of Indian institutions which conduct mathematical research: A study from the perspective of social network analysis

KR Kumar, S Manuel

Scientometrics 117 (2), 1041-1051 2018 - Solid waste management in Nagpur, India: The bin-free city

C Cheeseman, S Kumar, S Arya

Elsevier 2018 - Spectrum of (k, r)-regular hypergraphs

KR Kumar, RP Varghese

International Journal of Mathematical Combinatorics 2, 52 2017 - The m-ranking of nodes in complex networks

KR Kumar, S Manuel, D Benson

2017 9th International Conference on Communication Systems and Networks 2017 - Personal influence on the spreading of information: A network based study

KR Kumar, S Manuel

IJMTT 52, 570-573 2017 - Interior exterior and boundary of fuzzy soft multi topology in decision making

KR Kumar, SA Naisal

2016 International Conference on Control, Instrumentation, Communication and 2016 - 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 - An investment decision dilemma

S Mukherjee, MD Prasad, SS Kumar

Emerald Emerging Markets Case Studies 2016 - Mathematical modeling of consciousness: Subjectivity of mind

KR Kumar

2016 International Conference on Circuit, Power and Computing Technologies 2016 - Spectra of a new join of two graphs

RP Varghese, KR Kumar

Advances in Theoretical and Applied Mathematics 11 (4), 459-470 2016 - A MATHEMATICAL MODELING OF AYURVEDA DOSHAS: APPLICATION OF FUZZY SOFT TOPOLOGY

SA Naisal, KR Kumar

International Journal of Pure and Applied Mathematics 106 (8), 33-43 2016 - Detection of Fake Accounts in Social Network

S Kumar, RG Kumar, RKG Tekchandani

2015 - Social Network A New Perspective in Mathematical Epidemiology

VR Pravitha, KR Kumar

International Journal of New Technology and Research 1 (4) 2015 - How does consciousness overcome combinatorial complexity?

R Kumar

Artificial Intelligence and Evolutionary Algorithms in Engineering Systems 2015 - Role of non-governmental organisations in formation and linkage of self help groups in Punjab

SS Devi, S Kumar, J Singh

Indian Journal of Economics and Development 10 (2), 184-190 2014

- Efficient Domination in Circulant Graphs

GMG K. Reji Kumar

Discrete Mathematics 313, 767–771 2013

Citations: 29 - 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: 10 - Basic minimal dominating functions

KR Kumar, S Arumugam

Utilitas Mathematica 77, 235 2008

Citations: 7 - 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: 7 - Spectra of a new join of two graphs

RP Varghese, KR Kumar

Advances in Theoretical and Applied Mathematics 11 (4), 459-470 2016

Citations: 5 - Modeling of consciousness: classification of models

KR Kumar

Advanced Studies in Biology 3, 141-146 2010

Citations: 5 - 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: 4 - Collaborations of Indian institutions which conduct mathematical research: A study from the perspective of social network analysis

KR Kumar, S Manuel

Scientometrics 117 (2), 1041-1051 2018

Citations: 3 - Spectrum of (k, r)-regular hypergraphs

KR Kumar, RP Varghese

International Journal of Mathematical Combinatorics 2, 52 2017

Citations: 3 - Personal influence on the spreading of information: A network based study

KR Kumar, S Manuel

IJMTT 52, 570-573 2017

Citations: 3 - On maximal fractional independent sets in graphs

KR Kumar, S Arumugam, G MacGillivray

Ars Combinatoria 87, 205-212 2008

Citations: 3 - Mathematical modeling of consciousness: Subjectivity of mind

KR Kumar

2016 International Conference on Circuit, Power and Computing Technologies 2016

Citations: 2 - A MATHEMATICAL MODELING OF AYURVEDA DOSHAS: APPLICATION OF FUZZY SOFT TOPOLOGY

SA Naisal, KR Kumar

International Journal of Pure and Applied Mathematics 106 (8), 33-43 2016

Citations: 2 - Social Network A New Perspective in Mathematical Epidemiology

VR Pravitha, KR Kumar

International Journal of New Technology and Research 1 (4) 2015

Citations: 2 - How does consciousness overcome combinatorial complexity?

R Kumar

Artificial Intelligence and Evolutionary Algorithms in Engineering Systems 2015

Citations: 2 - Structure of the set of all minimal total dominating functions of some classes of graphs

K Kumar, G MacGillivray

Discussiones Mathematicae Graph Theory 30 (3), 407-423 2010

Citations: 2 - Spectra of a New Join in Duplication Graph

KR Kumar, RP Varghese

Mathematical Combinatorics, 53 2018

Citations: 1 - Interior exterior and boundary of fuzzy soft multi topology in decision making

KR Kumar, SA Naisal

2016 International Conference on Control, Instrumentation, Communication and 2016

Citations: 1 - Convexity of Minimal Dominating Functions and Minimal Edge Dominating Functions

KR Kumar

Lecture Notes Series, 97 2008

Citations: 1 - Topological Properties of the Set of All Minimal Dominating Functions of Graphs

KR Kumar

Proc. of ICDM, 249-254 2006

Citations: 1