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Solution To Some Open Problems On E-Super Vertex Magic Total Labeling Of Graphs, G. Marimuthu, M. S. Raja Durga, G. D. Devi

Applications and Applied Mathematics: An International Journal (AAM)

Let G be a finite graph with p vertices and q edges. A vertex magic total labeling is a bijection f from V(G)∪E(G) to the consecutive integers 1, 2, ..., p+q with the property that for every u∈V(G) , f( u)+ ∑f(uv)=K for some constant k. Such a labeling is E-super if f :E(G)→{1, 2,..., q}. A graph G is called E-super vertex magic if it admits an E-super vertex magic labeling. In this paper, we solve two open problems given by Marimuthu, Suganya, Kalaivani and Balakrishnan (Marimuthu et al., 2015).