• CYCLE RELATED MAGIC GRAPHOIDAL GRAPHS

Abstract

B. D. Acharya and E. Sampathkumar [1] defined Graphoidal cover as partition of edge set of G into internally disjoint paths (not necessarily open). The minimum cardinality of such cover is known as graphoidal covering number of G. Let G = (V, E) be a graph and let ψ be a graphoidal cover of G. Define f: V ∪ E → {1, 2, 3, ..., p + q} such that for every path P = (v₀v₁v_2…v_n) in ψ with f*(P) = f(v₀) + f(v_n) + = k, a constant, where f* is the induced labeling on ψ. Then, we say that G admits ψ - magic graphoidal total labeling of G. A graph G is called magic graphoidal if there exists a minimum graphoidal cover ψ of G such that G admits ψ - magic graphoidal total labeling. In this paper, we proved that C_n P₁, B₃^t, G_n, S(C_n K₁) and S(C_n × K₂) are magic graphoidal.