Graph theory was first introduced by Leonhard Euler in 1736 and still being one of the mathematic's topics which is rapidly developing and can be used to simplify mathematic problems. There are many interesting topics in graph theory; one of them is graph labeling. There are many ways of labeling a graph, and one of them is graceful labeling. Let G(V, E is a graph. The injective mapping f: V → {0,1, ..., |E|} is called graceful if the weights of edge w(uv) = |f(u) - f(v)| are all different for every edge uv. There is a famous conjecture in graceful labeling. It is said that all trees are graceful. To prove this conjecture, then we must show that every tree is graceful. There are many research papers dealing with the special cases of trees. Many classes of trees have been proven graceful, and one of them is supercaterpillar. Previous research had proved that supercaterpillars with certain conditions are also graceful. In this paper, we generalize the concept of supercaterpillar, and show that the subclass of supercaterpillar graphs that has not been discussed earlier is also graceful, using an adjacency matrix for the construction.
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