Divya K. Jadeja

Department of Mathematics,Saurashtra University,Rajkot, Gujarat (INDIA)E-mail:divyajadeja89@gmail.com

V. J. Kaneria

Department of Mathematics,Saurashtra University,Rajkot, Gujarat (INDIA)E-mail: kaneriavinodray@gmail.com

In 1967 Rosa defined graceful labeling and *α*-labeling. A graph G, a graceful labeling *f* is called *α*-labeling if there is a non-negative integer *k*(0 ≤ *k* ≤ |*E*(*G*)|) such that min{*f*(*u*), *f*(*v*)} ≤ $k<max\{f(u),f(v)\},\mathrm{\forall}uv\u03f5E(G).$ Here we call a graph G which admits a *α* -labeling as a *α*-graceful graph. A vertex *v* ∈ *V*(*G*) is called an extreme vertex for G, if there is an *α* -graceful labeling *f* on G such that *f*(*v*) = 0. A graph G is called a universal *α*-graceful graph if all of its vertices ...

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