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 New classes of graphs with edge $ \; \delta- $ graceful labeling

2022 ◽  
Vol 7 (3) ◽  
pp. 3554-3589
Author(s):  
Mohamed R. Zeen El Deen ◽  
◽  
Ghada Elmahdy ◽  
Keyword(s):  
Positive Integer ◽  
Mathematical Models ◽  
Communication Networks ◽  
Data Security ◽  
Coding Theory ◽  
Graph Labeling ◽  
Graceful Labeling ◽  
Extensive Range ◽  
Fan Graph ◽  
Positive Integers

<abstract><p>Graph labeling is a source of valuable mathematical models for an extensive range of applications in technologies (communication networks, cryptography, astronomy, data security, various coding theory problems). An edge $ \; \delta - $ graceful labeling of a graph $ G $ with $ p\; $ vertices and $ q\; $ edges, for any positive integer $ \; \delta $, is a bijective $ \; f\; $ from the set of edge $ \; E(G)\; $ to the set of positive integers $ \; \{ \delta, \; 2 \delta, \; 3 \delta, \; \cdots\; , \; q\delta\; \} $ such that all the vertex labels $ \; f^{\ast} [V(G)] $, given by: $ f^{\ast}(u) = (\sum\nolimits_{uv \in E(G)} f(uv)\; )\; mod\; (\delta \; k) $, where $ k = max (p, q) $, are pairwise distinct. In this paper, we show the existence of an edge $ \; \delta- $ graceful labeling, for any positive integer $ \; \delta $, for the following graphs: the splitting graphs of the cycle, fan, and crown, the shadow graphs of the path, cycle, and fan graph, the middle graphs and the total graphs of the path, cycle, and crown. Finally, we display the existence of an edge $ \; \delta- $ graceful labeling, for the twig and snail graphs.</p></abstract>

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 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 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
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