ISRN Discrete Mathematics

Volume 2012, Article ID 583671, 8 pages

http://dx.doi.org/10.5402/2012/583671

## Median Sets and Median Number of a Graph

Department of Computer Applications, Cochin University of Science and Technology, India

Received 30 September 2012; Accepted 18 October 2012

Academic Editors: H. Deng and P. Lam

Copyright © 2012 R. Ram Kumar and B. Kannan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A *profile* is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the *median* of the profile. Any subset of the vertex set such that it is the *median* of some profile is called a *median set*. The number of *median sets* of a graph is defined to be the *median number* of the graph. In this paper, we identify the median sets of various classes of graphs such as , for , and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established. We also express the median number of a product graph in terms of the median number of their factors.