GRAPHS WITH METRIC DIMENSION TWO - A CHARACTERIZATION

G. Sudhakara (India) and A. R. Hemanth Kumar (India)

Received July 8, 2009

References:

[1] F. Buckley and F. Harary, Distance in Graphs, Addison-Wesley, 1990. [2] Josĕ Cáceres, Carmen Hernando, Merće Mora, Ignacio M. Pelayo, Marìa L. Puertas, Carlos Seara and David R. Wood, On the metric dimension of Cartesian products of graphs, arXiv: math.CO/0507527 v3 2 Mar 2006. [3] F. Harary, Graph Theory, Narosa/Addison-Wesley, 1969. [4] F. Harary and R. A. Melter, On the metric dimension of a graph, Ars Combinatoria 2 (1976), 191-195. [5] Nora Hartsfield and Gerhard Ringel, Pearls in Graph Theory, Academic Press, USA, 1994. [6] Samir Khuller, Balaji Raghavachari and Azriel Rosenfeld, Landmarks in graphs, Discrete Appl. Math. 70(3) (1996), 217-229. [7] Christopher Poisson and Ping Zhang, The metric dimension of unicyclic graphs, J. Combin. Math. Combin. Comput. 40 (2002), 17-32. [8] B. Shanmukha, Certain applications of number theory in graphs with emphases to networks, Ph.D. Thesis, 2003. [9] B. Shanmukha, B. Sooryanarayana and K. S. Harinath, Metric dimension of wheels, Far East J. Appl. Math. 8(3) (2002), 217-229. [10] B. Sooryanarayana and B. Shanmukha, A note on metric dimension, Far East J. Appl. Math. 5(3) (2001), 331-339. [11] B. Sooryanarayana, Certain combinatorial connections between groups, graphs and surfaces, Ph.D. Thesis, 1998. [12] B. Sooryanarayana, On the metric dimension of a graph, Indian. J. Pure Appl. Math. 29(4) (1998), 413-415. [13] B. Sooryanarayana, K. S. Harinath and R. Murali, Some results on metric dimension of graph of diameter two, communicated. [14] Paul F. Tsuchiya, The landmark hierarchy: a new hierarchy for routing in very large networks, ACM 0-89791-279-9/88/008/0035, 1988, pp. 35-42.

Keywords and phrases: metric dimension, metric basis, distance partition.