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 [3], V4-cordial labeling is defined. It motivates 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 <₵, *> is an abelian 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.

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References

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3. L. Pandiselvi, Dr. S. Navaneethakrishnan, Dr. A. Nellai Murugan, Bi-Star V4 Cordial Graphs, IJASR, Vol 1, Issue 2; Feb 2016, pg no.14-21.