Abstract
The definition of edge-magic total labeling is that the sum of any edge and its associated points in a graph is equal to a certain constant, and the set satisfied by the value of midpoint and edge is from the number of one edge to the sum of the number of edges and points. In this paper, we design an edge-magic total labeling algorithm based on the hierarchical cascade graph. By using the edgemagic total labeling algorithm, we can get the super edgemagic total labeling of the hierarchical cascade graph. Through research and analysis, it is obtained that the join graph composed of hierarchical cascade graph, its extended graph and some special graphs is super edgemagic total labeling, super set-ordered edge-magic total labeling. Some theorems are summarized and proved.
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