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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