Graceful and Odd Graceful Labeling of Some Graphs

2013 ◽  
Vol 3 (1) ◽  
pp. 61
Author(s):  
S. K. Vaidya ◽  
N. H. Shah
Keyword(s):  
Graceful Labeling

Super Graceful Labeling for Some Simple Graphs

2012 ◽  
Vol 2 (1) ◽  
pp. 35 ◽  
Author(s):  
M. A. Perumal ◽  
S. Navaneethakrishnan ◽  
A. Nagaraja ◽  
S. Arockiaraj
Keyword(s):  
Graceful Labeling ◽  
Simple Graphs

Graceful and Odd Graceful Labeling of Graphs

2016 ◽  
Vol 6 (2) ◽  
pp. 13
Author(s):  
Ujwala Nilkanth Deshmukh
Keyword(s):  
Graceful Labeling

Graceful Labeling for Some Complete Bipartite Graph

2018 ◽  
Vol 9 (12) ◽  
pp. 2147-2152
Author(s):  
V. Raju ◽  
M. Paruvatha vathana
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Graceful Labeling

G-GRACEFUL LABELING OF GRAPHS

2020 ◽  
Vol 9 (4) ◽  
pp. 1973-1981
Author(s):  
A. Kumar ◽  
V. Kumar ◽  
K. Kumar ◽  
P. Gupta ◽  
Y. Khandelwal
Keyword(s):  
Graceful Labeling

scholarly journals Edge even graceful labeling of some corona graphs

2021 ◽  
Vol 1872 (1) ◽  
pp. 012007
Author(s):  
D Jayantara ◽  
Purwanto ◽  
S Irawati
Keyword(s):  
Graceful Labeling ◽  
Corona Graphs

scholarly journals Graceful labeling on a multiple-fan graph with pendants

2021 ◽  
Author(s):  
A. Akerina ◽  
K. A. Sugeng
Keyword(s):  
Graceful Labeling ◽  
Fan Graph

scholarly journals Infinitely many equivalent versions of the graceful tree conjecture

2015 ◽  
Vol 9 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Tao-Ming Wang ◽  
Cheng-Chang Yang ◽  
Lih-Hsing Hsu ◽  
Eddie Cheng
Keyword(s):  
Perfect Matching ◽  
Absolute Difference ◽  
Extra Condition ◽  
Graceful Labeling ◽  
The Absolute

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.

Graceful labeling on twig diamond graph with pendant edges*

2020 ◽  
Vol 39e (2) ◽  
pp. 188-192
Author(s):  
J. Jeba Jesintha ◽  
K. Subashini ◽  
Allu Merin Sabu
Keyword(s):  
Graceful Labeling

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

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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