 Qualification:
Ph.D, MSc
Email:
kn_geetha@blr.amrita.edu
Phone:
9980204500

Dr.Geetha is working as an Assistant Professor in the Department of Mathematics from 2007. She has a vast teaching experience of 18 years  (including Amrita) serving in various colleges in Karnataka that includes the experience in National Institute of Technology, Surathkal.She has obtained her Doctorate degree from Visvesvaraya Technological University, Belgaum in the year 2014. Her areas of interest are Discrete Mathematics and Graph Theory.

## Qualification

Degree University Year
Ph.D.(Graph Theory) VTU, Belgaum 2014
M.Sc. Mathematics Bangalore University 1997
B.Sc.  Bangalore University 1995

## Professional Appointments

Year Affiliation
Senior Lecturer / Assistant Professor/ Assistant Professor (SG) (Since2007)      Amrita Vishwa Vidyapeetham, Bengaluru Campus
Lecturer/ Senior Lecturer (2000 -2007)     Vemana Institute of Technology, Bengaluru.
Lecturer 26/10/1998 to 31/07/2000     National Institute of Technology, Surathkal, Karnataka
Lecturer 1/06/1997 to 31/03/1998     SJR College for Women, Bengaluru.

• 13 years

## Major Research Interests

• Graph Theory
• Discrete Mathematics
• Optimization

## Publications

### Publication Type: Journal Article

Year of Publication Title

2017

Dr. Geetha K. N. and Sooryanarayana, Bb, “2-Metric dimension of cartesian product of graphs”, International Journal of Pure and Applied Mathematics, vol. 112, pp. 27-45, 2017.[Abstract]

Let G(V,E) be a connected graph. A subset S of V is said to be 2-resolving set of G, if for every pair of distinct vertices u, v /∈ S, there exists a vertex w ∈ S such that |d(u,w) - d(v,w)| ≥ 2. Among all 2-resolving sets of G, the set having minimum cardinality is called a 2-metric basis of G and its cardinality is called the 2-metric dimension of G and is denoted by βk(G). In this paper, we determine the 2-metric dimension of cartesian product of complete graph with some standard graphs. Further, we have determined the 2-metric dimension of the graphs Pm Pn, Cm Pn and Cm Cn. © 2017 Academic Publications, Ltd.

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2015

N. Na Swamy, Sooryanarayana, Bb, Swamy, G. KcNanjunda, and Dr. Geetha K. N., “Open neighborhood chromatic number of an antiprism graph”, Applied Mathematics E - Notes, vol. 15, pp. 54-62, 2015.[Abstract]

<p>An open neighborhood k-coloring of a simple connected undirected graph G(V,E) is a k-coloring c: V → {1, 2, …, k}, such that, for every w ∈ V and for all u, v ∈ N(w), c(u) ≠ c(v). The minimum value of k for which G admits an open neighborhood k-coloring is called the open neighborhood chromatic number of G denoted by χonc(G). In this paper, we obtain the open neighborhood chromatic number of the Petersen graph. Also, we determine this number for a family of graphs called antiprism graphs. © 2015, Applied Mathematics E-Notes.</p>

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2014

B. Sooryanarayana and Dr. Geetha K. N., “On the k-Metric Dimension of Graphs”, Journal of Mathematics and Computational Science, vol. 4, no. 5, pp. 861–878, 2014.[Abstract]

Let G(V,E) be a connected graph. A subset S of V is said to be k-resolving set of G, if for every pair of distinct vertices u, v ∈/ S, there exists a vertex w ∈ S such that |d(u,w)−d(v,w)| ≥ k, for some k ∈ Z +. Among all k-resolving sets of G, the set having minimum cardinality is called a k-metric basis of G and its cardinality is called the k-metric dimension of G and is denoted by βk(G). In this paper, we have discussed some characterizations of k-metric dimension in terms of some graphical parameters. We have mainly focused on 2-metric dimension of graphs and discussed few characterizations. Further 2-metric dimension of trees is determined and from this result 2- metric dimension of path, cycle and sharp bounds of unicyclic graphs are established

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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. 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.

## Courses taught

• Discrete Mathematics
• Probability and Statistics
• Probability and Random Processes
• Linear Algebra
• Numerical Analysis
• Optimization
• Complex analysis
• Integral Transforms
• Partial differential equations
• Single variable calculus
• Multivariable Calculus
• Matrix Algebra
• Differential equations
• Laplace Transforms
• Graph Theory.
Faculty Research Interest: