Abstract
Graceful labeling is one of the interesting topics in graph theory. Let G(V, E) is a graph. The injective mapping f: V → {0, 1, …, |E|} is called graceful if the weight of edge w(uv) = |f(u) − f(v)| are all different for every edge uv. The famous conjecture in graceful labeling is “all trees are graceful”. Previous research had proved that caterpillar graph is graceful. There also a research that has introduced the supercaterpillar graph and already proved supercaterpillar satisfying certain conditions are also graceful. In this paper, we generalized the concept of supercaterpillar and show subclass of supercaterpillar graph that has not been discussed earlier is also graceful.
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