Abstract
A graph G with ∣ E (G) ∣ = q, an injective function f: V(G)→{0, 1, 2, g, q} is a β -labeling of G provided that the values f (u) - f (v) for the q pairs of adjacent vertices u and v are distinct. A β-labeling is also known as a graceful labeling. It has been conjectured that every tree is graceful. In this paper, we define graceful labeling for a tree constructed from caterpillars.
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