Graceful Labeling in the Context of Duplication of Graph Elements

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Siwaporn Saewan
Thanapa Khanwman
Waraporn Dangnapaponkul
Sumita Kaewthong

Abstract

Let a simple graph G = ((V (G), E(G)) be connected and undirected graph with p vertices and q edges. Let f be a function from the set of vertices to the set of integer {0,1 , 2, 3,…, q} and let f* be a function from the set of edge to the set of positive integer {1, 2, 3,…, q} defined as


  f*(uv) = |f(u) − f(v)|  


for all u,v∈V (G) and uv∈E(G) . A function f is called graceful labeling of a graph G if f is injective and f* is bijective. The graph G which admits graceful labeling f is called a graceful graph. In this paper, we find graceful labeling for some new graphs results from the duplication of graph elements and then we prove that the new graphs are graceful.

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References

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