Recent Advancements in Graph Theory

3Universal α-graceful Gear related Graphs

Divya K. Jadeja

Department of Mathematics,Saurashtra University,Rajkot, Gujarat (INDIA)E-mail:[e-mail]

V. J. Kaneria

Department of Mathematics,Saurashtra University,Rajkot, Gujarat (INDIA)E-mail: [e-mail]

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)},∀uvϵE(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 ...