Abstract

Mod(k) Vertex Magic Labeling of Some Hamiltonian Graphs

P. Sumathi1 and B. Fathima2*

1Department of Mathematics, C.K.N College, Chennai-600 102, INDIA. 2Research Scholar, Department of Mathematics, C.K.N College, Chennai-600 102, INDIA. *Assistant Professor, Department of Mathematics (F.N), J.B.A.S College for Women, Teynampet, Chennai-600 018, INDIA.

ABSTRACT

Let G be a simple, undirected and non trivial graph containing p vertices and q edges. For any integer k≥2, l ∈Zk, there exists an injective function f:V(G)→{ [𝑘/2], [𝑘/2]+𝑙, [𝑘/2]+𝑙+1,...,[𝑘/2]+k(p-1)} such that for every edge (e=uv)𝜖E(G), the mapping f*: E(G) → Zk defined by f*(uv)=(f(u)+f(v))(mod k)= l is a constant mapping. The function f is said to be a Mod(k) vertex magic labeling of G. A graph G is called Mod(k) vertex magic graph if it admits a Mod(k) vertex magic labeling. In this paper, it is shown that the some Hamiltonian graphs namely Flower graph, n-crossed prism are Mod(k) vertex magic graphs. AMS Subject Classification: 05C78.

Keywords :Mod(k)vertex magic labeling, Hamiltonian graph, Flower graph, n-crossed prism.

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