Journal of Prime Research in Mathematics

# Sum divisor cordial labeling for path and cycle related graphs

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

$$^{1}$$Corresponding Author: lourdusamy15@gmail.com

### 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.