Abstract

A graceful labeling of a graph G with q edges is an injection f : V (G) → {0,1,2,...,q} with the property that the resulting edge labels are also distinct, where an edge incident with the vertices u and v is assigned the label |f(u)-f(v)|. A graph which admits a graceful labeling is called a graceful graph. In this paper, we prove that the path union of vertex switching of even cycles in increasing order is graceful.

Keywords and Phrases

Graceful labeling, vertex switching, Path union of graphs.

A.M.S. subject classification

05C78.

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