**Journal of Prime Research in Mathematics**

Vol. 1 (2015), Issue 1, pp. 123 – 136

ISSN: 1817-3462 (Online) 1818-5495 (Print)

ISSN: 1817-3462 (Online) 1818-5495 (Print)

# Existence and non existence of mean cordial labeling of certain graphs

**R. Ponraj
**Department of Mathematics, Sri Paramakalyani College, Alwarkurichi-627 412, Tamil Nadu, India.

**Department of Mathematics, Sri Paramakalyani College, Alwarkurichi-627 412, Tamil Nadu, India.**

S. Sathish Narayanan

S. Sathish Narayanan

\(^{1}\)Corresponding Author: ponrajmaths@gmail.com

Copyright © 2015 R. Ponraj, S. Sathish Narayanan. 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.

**Published:**December, 2015.

### Abstract

Let f be a function from the vertex set \(V (G)\) to \({0, 1, 2}\). For each edge \(uv\) assign the label \(\frac{f(u)+f(v)}{2}\). \(f\) is called a mean cordial labeling if \(|v_f (i) − v_f (j)| ≤ 1\) and \(|e_f (i) − e_f (j)| ≤ 1\), \(i, j ∈ {0, 1, 2}\), where \(v_f (x)\) and \(e_f (x)\) respectively denote the number of vertices and edges labeled with \(x\) \((x = 0, 1, 2)\). A graph with a mean cordial labeling is called a mean cordial graph. In this paper we investigate mean cordial labeling behavior of prism, \(K_2 +\overline{K_m}\), \(K_n + \overline{2K_2}\), book \(B_m\) and some snake graphs.

#### Keywords:

Prism, corona, flower graph, complete graph, path.