Journal of Prime Research in Mathematics

# 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.
S. Sathish Narayanan
Department of Mathematics, Sri Paramakalyani College, Alwarkurichi-627 412, Tamil Nadu, India.

$$^{1}$$Corresponding Author: ponrajmaths@gmail.com

### 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.