# Title

2-METRIC DIMENSION OF
CARTESIAN PRODUCT OF GRAPHS

# Authors

K.N. Geetha, B. Sooryanarayana
Department of Mathematics
Amrita Vishwa Vidyapeetham
Amrita School of Engineering
Bangalore, Karnataka State, INDIA
Deptartment of Mathematical and Computational Studies
Dr. Ambedkar Institute of Technology
Bangalore, Karnataka State, INDIA

# Abstract

Let be a connected graph. A subset of is said to be 2-resolving set of , if for every pair of distinct vertices , there exists a vertex such that . Among all -resolving sets of , the set having minimum cardinality is called a 2-metric basis of and its cardinality is called the 2-metric dimension of and is denoted by . 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 , and .

# History

Revised: November 22, 2016
Published: January 26, 2017

# AMS Classification, Key Words

AMS Subject Classification: 05C12
Key Words and Phrases: cartesian product, 2-metric basis, 2-metric dimension

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# How to Cite?

DOI: 10.12732/ijpam.v112i1.2 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 112
Issue: 1
Pages: 27 - 45