• GRACEFUL LABELING OF THE PATHS USING PADAVON SEQUENCE

Abstract

A(p, q) connected graph is padavon graceful graph if there exists an injective map f: E(G)→{1,1,1,2,2,3,4,5,7,…,2q-1}  so that induced map f_{+ :} V(G) → {0, 1, …,p+1} defined by f₊(x) = |f(u)-f(v)| where the vertex x is incident with other vertex y and makes all the edges distinct. In this article, the padavon gracefulness of paths p_1, p_2, p_3… p₁₂ ­is obtained.