Qualification:
Ph.D, MPhil, MSc
kn_meera@blr.amrita.edu
Phone:
9449153772

Dr K N Meera has been working in the Department of Mathematics, Amrita School of Engineering Bengaluru since 2005.  She has completed her Post Graduation degree in Mathematics from Bangalore university and Ph. D from Dravidian University. Topic of her thesis is  “Strict boundary vertices, Radiatic dimension and Optimal outer sum number of certain classes of graphs”  in graph theory. Research interests includes Graph theory and probability.

## Qualification

Degree University Year
Ph.D Dravidian 2015
M.Sc. Bangalore 1996

## Professional Appointments

Year Affiliation
Assistant Professor(2007 onwards)     Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru
Senior Lecturer(2006-2007)     Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru
Lecturer(2005-2006)     Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru
Lecturer(2002-2005)     The Oxford College of Engineering, Bangalore
Lecturer(1999-2002)     BTL Institute of Technology, Bangalore
Lecturer(1996-1999)     Maharani Lakshmi Ammanni college for women,Bangalore

• 10 years

• Graph theory

## Membership in Professional Bodies

• Member of Academy of Discrete Mathematics and applications
• Member of Ramanujan Mathematical society

## Publications

### Publication Type: Journal Article

Year of Publication Title

2020

Giriraja C. V., Chirag V., Sudheendra C., S., B. Samarth, Dr. T. K. Ramesh, and Dr. K. N. Meera, “Priority Based Time-Division Multiple Access Algorithm for Medium Range Data Communication in Very High Frequency Radios”, Journal of Computational and Theoretical Nanoscience, Volume 17, Number 1, vol. 17, Number 1, 2020.[Abstract]

In this paper, A novel and efficient time division multiple access (TDMA) algorithm for military last-mile data communication is designed. A dynamic slot assignment method coupled with an out-of-band control mechanism is used for the proposed design. In out-of-band, there is a well-defined control segment along with the data segment. So, if a new node specifically a high priority node arrives at the network, it can signal its arrival by a response in the designated mini-slots and can also check the slot in the network, if no idle slots are available. Assigning priority to the nodes would also ensure the delivery of the important messages first. Query messages are broadcasted by the Central node in order to detect new nodes. This reduces nodes working time and also ensures that the nodes don’t interrupt any existing communication. Furthermore, we describe the feasibility and the reliability of this algorithm for military’s last-mile (end user) data communication.

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2019

Y. Lavanya, Dhanyashree,, and Dr. K. N. Meera, “Radio Mean graceful graphs”, Journal of Physics, vol. 1172(1) 012071, 1-10 , 2019.[Abstract]

A Radio Mean labeling of a simple, finite, undirected and connected graph G is a one to one map f:V(G) → N such that for two distinct vertices u and v of $G,d(u,v)+\left|\frac{f(u)+f(v)}{2}\right|\ge 1+diam\,(G)$. The radio mean number of f, rmn(f), is the highest number assigned to any vertex of G. The radio mean number of G,rmn(G), is the minimum value of rmn(f), taken over all radio mean labelings of G. If rmn(G) = |V(G)|, we call such graphs as radio mea graceful. In this paper, we find the radio mean number of subdivision graph of complete graphs, Mongolian tent graphs, subdivision of friendship graphs and Diamond graphs and prove that these graphs are radio mean graceful.

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2014

Dr. Geetha K. N., Dr. K. N. Meera, Swamy, N. Narasimha, and Sooryanarayana, B., “Open Neighborhood Coloring of Prisms”, Journal of Mathematical and Fundamental Sciences, vol. 45, pp. 245–262, 2014.[Abstract]

For a simple, connected, undirected graph G(V, E) an open neighborhood coloring of the graph G is a mapping f : V (G) --> Z+ such that for each w in V(G), and for all u, v in N(w), f(u) is different from f(v). The maximum value of f(w), for all w in V (G) is called the span of the open neighborhood coloring f. The minimum value of span of f over all open neighborhood colorings f is called open neighborhood chromatic number of G, denoted by Xonc(G). In this paper we determine the open neighborhood chromatic number of prisms.

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2013

Dr. K. N. Meera and Sooryanarayana, B., “Strict boundary vertices of a graph”, Advances and applications in discrete mathematics, vol. 12, no. 1, pp. 61–72, 2013.[Abstract]

Let G be a simple connected graph. A vertex v of G is said to be a boundary vertex of another vertex u of G if d(w, u) ≤ d(u, v) for each neighbor w of v. If a vertex v is a boundary vertex of any vertex u of G, then it is said to be a boundary vertex of the graph G. In this paper, we define a vertex v of G to be a strict boundary vertex of
another vertex u of G if d(w, u) < d(u, v) for each neighbor w of v. If a vertex v is a strict boundary vertex of any vertex u of G, then it is said to be a strict boundary vertex of the graph G. In this paper, we study the properties of strict boundary vertices of a graph.

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2013

Dr. Geetha K. N., Dr. K. N. Meera, N, N., and Sooryanarayana, B., “Open neighborhood coloring of graphs”, International journal of contemporary mathematical sciences, vol. 8, pp. 13–16, 2013.

2012

Dr. K. N. Meera and Sooryanarayana, B., “Radiatic dimension of a graph”, Journal of computations and modelling, vol. 2, no. 4, pp. 109–131, 2012.[Abstract]

Let G(V, E) be a simple, finite, connected graph. An injective mapping f : V (G) → Z + such that for every two distinct vertices u, v ∈ V (G), |f(u) − f(v)| ≥ diam(G) + 1 − d(u, v) is called a radio labeling of G. The radio number of f, denoted by rn(f) is the maximum number assigned to any vertex of G. The radio number of G, is the minimum value of rn(f) taken over all radio labelings f of G. A graph G on n vertices is radio graceful if and only if rn(G) = n. In this paper, we define the radiatic dimension of G to be the smallest
positive integer k, such that the sequence of injective functions fi: V (G) → {1, 2, 3, . . . , n}, 1 ≤ i ≤ k, satisfy the condition that for every two distinct vertices u, v ∈ V (G), |fi(u)−fi(v)| ≥ diam(G)+ 1−d(u, v) for some i and denote it by rd(G). Hence a graph is radio graceful if and only if rd(G) = 1. In this paper we study the radiatic dimension of some standard g

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2011

Dr. K. N. Meera and Sooryanarayana, B., “Optimal Outer sum number of a graph”, International Journal of combinatorial graph theory and applications, vol. 4, no. 1, pp. 23–35, 2011.

### Publication Type: Conference Paper

Year of Publication Title

2018

R. R. Vanam and Dr. K. N. Meera, “Radio degree of a graph”, in AIP Conference Proceedings, 2018, vol. 1952.[Abstract]

A labeling f: V (G) → Z+ such that |f(u) - f(v)|≥diam(G) + 1 - d(u, v) holds for every u, v ϵ V (G), is called a radio labeling of G. We define the radio degree of a labeling f: V (G) → {1, 2, ⋯ |V (G)|} as the number of pairs of vertices u, v ϵ V (G) satisfying the condition |f(u) - f(v)|≥diam(G) + 1 - d(u, v) and denote it by rdeg(f). The maximum value of rdeg(f) taken over all such labelings is defined as the radio degree of the graph denoted by rdeg(G). In this paper, we find the radio degree of some standard graphs like paths, cycles, complete graphs, complete bipartite graphs and also obtain a characterization of graphs of diameter two that achieve the maximum radio degree. © 2018 Author(s).

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Research scholars
Year Funding Agency Title of the Project Investigators Status
2019 DST SERB Radiatic dimension of product graphs Dr. K. N. Meera Completed

## Courses taught

• Probability and Random Process
• Linear Algebra
• Graph theory
• Discrete Mathematics
• Matrix algebra and Calculus
• Vector calculus and ordinary differential equations

## Student Guidance

Research scholars
Sl.No. Name of the Student(s) Topic Status – Ongoing/Completed Year of Completion
1. Dhanyashree Radio path coloring of graphs. Ongoing
2. Meera Saraswathi. Radio mean graceful graphs. Ongoing

Faculty Research Interest: