Edge even graceful labeling of some corona graphs

A graceful labeling of a graph with q edges is a labeling of its vertices using the integers in [0, q], such that no two vertices are assigned the same label and each edge is uniquely identified by the absolute difference between the labels of its endpoints. The well known Graceful Tree Conjecture (GTC) states that all trees are graceful, and it remains open. It was proved in 1999 by Broersma and Hoede that there is an equivalent conjecture for GTC stating that all trees containing a perfect matching are strongly graceful (graceful with an extra condition). In this paper we extend the above result by showing that there exist infinitely many equivalent versions of the GTC. Moreover we verify these infinitely many equivalent conjectures of GTC for trees of diameter at most 7. Among others we are also able to identify new graceful trees and in particular generalize the ?-construction of Stanton-Zarnke (and later Koh- Rogers-Tan) for building graceful trees through two smaller given graceful trees.

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On Graceful Labeling of the Generalization of Cyclic Snakes

Journal of Discrete Mathematical Sciences and Cryptography ◽

10.1080/09720529.2014.1001589 ◽

2015 ◽

Vol 18 (6) ◽

pp. 773-783 ◽

Cited By ~ 2

Author(s):

E. M. Badr

Keyword(s):

Graceful Labeling

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Graceful labeling on twig diamond graph with pendant edges*

Bulletin of Pure & Applied Sciences- Mathematics and Statistics ◽

10.5958/2320-3226.2020.00018.1 ◽

2020 ◽

Vol 39e (2) ◽

pp. 188-192

Author(s):

J. Jeba Jesintha ◽

K. Subashini ◽

Allu Merin Sabu

Keyword(s):

Graceful Labeling

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Graceful Labeling and Skolem Graceful Labeling on the U-star Graph and It’s Application in Cryptography

Jambura Journal of Mathematics ◽

10.34312/jjom.v3i2.9992 ◽

2021 ◽

Vol 3 (2) ◽

pp. 103-114

Author(s):

Meliana Pasaribu ◽

Yundari Yundari ◽

Muhammad Ilyas

Keyword(s):

Star Graph ◽

Graceful Labeling ◽

Injective Function ◽

Bijective Function ◽

Labeling Pattern

Graceful Labeling on graph G=(V, E) is an injective function f from the set of the vertex V(G) to the set of numbers {0,1,2,...,|E(G)|} which induces bijective function f from the set of edges E(G) to the set of numbers {1,2,...,|E(G)|} such that for each edge uv e E(G) with u,v e V(G) in effect f(uv)=|f(u)-f(v)|. Meanwhile, the Skolem graceful labeling is a modification of the Graceful labeling. The graph has graceful labeling or Skolem graceful labeling is called graceful graph or Skolem graceful labeling graph. The graph used in this study is the U-star graph, which is denoted by U(Sn). The purpose of this research is to determine the pattern of the graceful labeling and Skolem graceful labeling on graph U(Sn) apply it to cryptography polyalphabetic cipher. The research begins by forming a graph U(Sn) and they are labeling it with graceful labeling and Skolem graceful labeling. Then, the labeling results are applied to the cryptographic polyalphabetic cipher. In this study, it is found that the U(Sn) graph is a graceful graph and a Skolem graceful graph, and the labeling pattern is obtained. Besides, the labeling results on a graph it U(Sn) can be used to form a table U(Sn) polyalphabetic cipher. The table is used as a key to encrypt messages.

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