**Journal of Prime Research in Mathematics**

Vol. 1 (2019), Issue 1, pp. 101 – 114

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

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

**Sum divisor cordial labeling for path and cycle related graphs**

**A. Lourdusamy
**Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai 627 002 , India.

**Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai 627 002 , India.**

F. Patrick

F. Patrick

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

Copyright © 2019 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, 2019.

### Abstract

A sum divisor cordial labeling of a graph \(G\) with vertex set \(V\) is a bijection \(f\) from \(V\) to \(\{1, 2, ··· , |V (G)|\}\) such that an edge \(uv\) is assigned the label 1 if 2 divides \(f(u) + f(v)\) and \(0\) otherwise; and the number of edges labeled with \(0\) and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial graph. In this paper, we prove that \(P^{2}_{n}, P_n ⊙ mK_1, S(P_n ⊙ mK_1), D_2(P_n), T(P_n)\), the graph obtained by duplication of each vertex of path by an edge, \(T(C_n), D_2(C_n)\), the graph obtained by duplication of each vertex of cycle by an edge, C^{(t)}_{4}, book, quadrilateral snake and alternate triangular snake are sum divisor cordial graphs.

#### Keywords:

Sum divisor cordial, divisor cordial.