Vertex-magic total labelings of union of generalized Petersen graphs and union of special circulant graphs

摘要

Let G be a graph with vertex set V = V{G) and edge set E = E(G), and let n = |V(G)| and e = |E(G)|. A vertex-magic total labeling (VMTL) of a graph is defined as a one-to-one mapping taking the vertices and edges onto the set of integers {1, 2,..., n + e}, with the property that the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex. In this paper, we present the vertex magic total labeling of disjoint union of t generalized Petersen graphs ∪_(j=1)~tP{n_j,m_j), and disjoint union of t special circulant graphs ∪_(j=1)~t(1, m_j).