GRACEFULNESS IN THE PATH UNION OF VERTEX SWITCHING OF EVEN CYCLES IN INCREASING ORDER

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.