**Journal of Prime Research in Mathematics**

Vol. 1 (2017), Issue 1, pp. 01 – 07

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

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

# Vertex equitable labeling for ladder and snake related graphs

**A. Lourdusamy
**Department of Mathematics, St.Xavier’s College, Palayamkottai-627002, India.

**Department of Mathematics, St.Xavier’s College, Palayamkottai-627002, India.**

F. Patrick

F. Patrick

\(^{1}\)Corresponding Author: lourdusamy15@gmail.com

Copyright © 2017 A. Lourdusamy, F. Patrick. 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, 2017.

### Abstract

Let \(G\) be a graph with p vertices and q edges and \(A = {0, 1, 2, · · · ,\frac{q}{2}}\). A vertex labeling \(f : V (G) → A\) induces an edge labeling \(f^∗\) defined by \(f^∗ (uv) = f(u) + f(v)\) for all edges \(uv\). For \(a ∈ A\), let \(v_f (a)\) be the number of vertices \(v\) with\( f(v) = a\). A graph \(G\) is said to be vertex equitable if there exists a vertex labeling f such that for all \(a\) and \(b\) in A, \(|v_f (a) − v_f (b)| ≤ 1\) and the induced edge labels are \({1, 2, 3, · · · , q}\). In this paper, we prove that triangular ladder \(T L_n, L_n ⊙ mK_1, Q_n ⊙ K_1, T L_n⊙K_1\) and alternate triangular snake \(A(T_n)\) are vertex equitable graphs.

#### Keywords:

Vertex equitable labeling, ladder, snake.