# Complex Composition Cordial Labeling of Complete and Complete Bipartite Graph

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Year:
2017
Type of Publication:
Article
Keywords:
Complex Composition Cordial Graph, Complex Composition Cordial Labeling
Authors:
R. MARIA IRUDHAYA ASPIN CHITRA; Dr. A. NELLAI MURUGAN
Journal:
IJISM
Volume:
5
Number:
3
Pages:
83-88
Month:
May
ISSN:
2347-9051
Abstract:
Let be any abelian group. A graph G= (V(G), E(G)) is said to be A-cordial if there is a mapping f:V(G)→A which satisfies the following two conditions with each edge e = uv is labeled as f*(uv) = f(u)*f(v) |v_f (a)- v_f (b) | ≤ 1 ∀ a, b ∈ A |e_f (a)- e_f (b) | ≤ 1 ∀ a, b ∈ A where v_f (a) = the number of vertices with label a v_f (b) = the number of vertices with label b e_f (a) = the number of edges with label a e_f (b) = the number of edges with label b In , V4-cordial labeling is defined. It mooted me an idea to define CCCL as follows. We have defined a set ₵={f_1, f_2, f_3, f_4} where f_1=z, f_2=-z, f_3=1/z, f_4=-1/z ∀ z ∈C-{0} is an abelian group and under binary operation * is defined as f_1* f_2 =f_1 ∘ f_2 =f_1(f_2). We note that if A= is a multiplicative group. Then the labeling is known as Complex Composition Cordial Labeling, and in short denoted as CCCL. A graph which admits CCCL is called as Complex Composition Cordial Graph, which is denoted as CCCG. In this paper, it is proved that Path P_n and Star S_n are Complex Composition Cordial graphs             