Some methods for constructing some classes of graceful uniform trees

I Nengah Suparta, I Dewa Made Agus Ariawan


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.


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

Full Text:



J.A. Gallian, A Dynamic Survey of Graph Labelling, Elect. J. Combinatorics (2017)

D. Morgan, All Lobsers with Perfect Matchings are Graceful. Article of Electronic Notes in Discrete Mathematics, Vol 11 (2002), pp.503–508.

K.M. Koh, D.G. Rogers and T. Tan, Products of graceful trees, Discrete Mathematics vol. 31 (1980), 279-292.

A. Munia, J. Maowa, S. Tania, M. Kaykobad, A New Class of Graceful Tree. International Journal of Engineering Sciences and Research, Vol 5 (2014), 1112–1115.

N. Ujwala, Applications of Graceful Graph. International Journal of Engineering Sciences and Research Technology, Vol 4 (2015), 129–131.

K. Wenger, Two Rosa-type Labeling of Uniform k-distant Trees and a New Class of Trees, Honors Projects in Mathematics of Illnois Wesleyan University (2015)

Sedlacek, Problem 27, in Theory of Graphs and its Applications, Proc. Symposium Smolenice, (1963) 163-167.



  • There are currently no refbacks.

ISSN: 2541-2205

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View IJC Stats