Some methods for constructing some classes of graceful uniform trees

I Nengah Suparta, I Dewa Made Agus Ariawan

Abstract


A tree T(V, E) is graceful if there exists an injective function f from the vertex set V(T) into the set {0, 1, 2, ..., ∣V∣ − 1} which induces a bijective function fʹ from the edge set E(T) onto the set {1, 2, ..., ∣E∣}, with fʹ(uv) = ∣f(u) − f(v)∣ for every edge {u, v} ∈ E. Motivated by the conjecture of Alexander Rosa (see) saying that all trees are graceful, a lot of works have addressed gracefulness of some trees. In this paper we show that some uniform trees are graceful. This results will extend the list of graceful trees.


Keywords


caterpillar; uniform caterpillar; uniform superlobster; uniform distant tree; graceful

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References


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DOI: http://dx.doi.org/10.19184/ijc.2018.2.2.7

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