Expanding Super Edge-Magic Graphs

E. T. Baskoro1¹, Y. M. Cholily^1,2

¹ Department of Mathematics, Institut Teknologi Bandung

Jl. Ganesa 10 Bandung 40132, Indonesia

Emails : {ebaskoro,yus}@dns.math.itb.ac.id

² Department of Mathematics, Universitas Muhammadiyah Malang

Jl. Tlogomas 246 Malang 65144, Indonesia

Email : yus@umm.ac.id

For a graph G, with the vertex set V(G) and the edge set E(G) an edge-magic total labeling is a bijection f from V(G) È E(G) to the set of integers {1,2,…,|V(G)|+|E(G)|} with the property that f(u)+f(v)+f(uv)=k for each uvÎE(G) and for a fixed integer k. An edge-magic total labeling f is called super edge-magic total labeling if f(V(G))={1,2,…, |V(G)|} and f(E(G))={|V(G)|+1, |V(G)|+2,…, |V(G)|+ |E(G)|}. In this paper we construct the expanded super edge-magic total graphs from cycles C_n, generalized Petersen graphs and generalized prisms.

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