      - Cordial labeling of Some Cycle Related Graphs

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American Journal of Engineering Research (AJER) 2016 American Journal of Engineering Research (AJER) e-ISSN: 2320-0847 p-ISSN : 2320-0936 Volume-5, Issue-10, pp-90-95 www.ajer.org Research Paper Open Access

 p  - Cordial labeling of Some Cycle Related Graphs  2  D. S. T. Ramesh1, K. Jenita Devanesam2 1

Department of Mathematics, Margoschis College, Nazareth – 628 617, Tamil Nadu, INDIA 2 Department of Mathematics, Pope’s College, Sawyerpuram-628251, Tamil Nadu, India.

 p  - cordial labeling of a graph G with p vertices is a bijection f: V(G)  {1, 2, 3,…, p}  2  1 if f (u)  f(v)   p    2  and e (0)  e (1)  1 . If a graph has  p  - cordial defined by f (e  uv)    2  0 otherwise  p  - cordial where  p  represents the nearest integer less than or equal to p labeling then it is called  2   2  2 ABSTRACT: A

f

f

 p  2  - co rd ial g raph for n ≥ 3 , excep t fo r n = 4 and the graph  p obtained by duplication of an arbitrary vertex by a new edge in cycle C n is  2  - co rd ia l and the graph  p obtained by duplication of an arbitrary edge by a new vertex in cycle Cn is  2  -cordial. By a graph we mean In th is p aper we p rove C n is

a finite, undirected graph without multiple edges or loops. For graph theoretic terminology, we refer to Harary [2] and Bondy [1].

Keywords:

p  2 

- cordial, cycle.

Definition1.1: Duplication of a vertex v k by a new edge e = vꞌvꞌꞌ in a graph G produces a new graph Gꞌ such that N(vꞌ) = {vk, vꞌꞌ} and N(vꞌꞌ) = {vk,vꞌ}. Definition1.2: Duplication of an edge e = uv by a new vertex w in a graph G produces a new graph Gꞌ such that N(w) = {u, v}. Theorem1.1: Cn is

 p  2  - cordial graph for n ≥ 3, except for n = 4.

Proof: Case(i): n = 4m, m = 2, 3, 4, … Let the vertices be u1, u2, …, un.

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