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Graceful Cascading Labelling Algorithm: Construction of Graceful Labelling of Trees

2021 2nd International Conference on Robotics, Electrical and Signal Processing Techniques (ICREST), 2021
The Graceful Labelling of trees is one of the most challenging conjectures in Graph Theory, proudly known as the ’Disease’ of Graph Theory which remains a challenge as it remains unsolved.
D. Gomes, M. Hasan
semanticscholar   +2 more sources

Graceful coloring is computationally hard

arXiv.org
Given a (proper) vertex coloring $f$ of a graph $G$, say $f\colon V(G)\to \mathbb{N}$, the difference edge labelling induced by $f$ is a function $h\colon E(G)\to \mathbb{N}$ defined as $h(uv)=|f(u)-f(v)|$ for every edge $uv$ of $G$.
Cyriac Antony, D. Laavanya, S. DeviYamini   +2 more
semanticscholar   +3 more sources

Graceful Labelling: State of the Art, Applications and Future Directions

Mathematics in Computer Science, 2011
L. Brankovic, Ian M. Wanless
semanticscholar   +3 more sources

FIBONACCI AND SUPER FIBONACCI GRACEFUL LABELLINGS OF SOME TYPES OF GRAPHS

Journal of Automation and Information Sciences, 2021
We consider the basic theoretical information regarding the Fibonacci graceful graphs. An injective function is said a Fibonacci graceful labelling of a graph of a size , if it induces a bijective function on the set of edges , where by the rule , for ...
M. Semenyuta
semanticscholar   +1 more source

Colligation of cycle graphs on one modulo N graceful labelling and its applications

Journal of Information and Optimization Sciences, 2019
A graph G is said to be one modulo N graceful (where N is a positive integer) if there is a function φ from the vertex set of G to {0, 1, N, (N + 1), 2N, (2N + 1), … , N(q – 1), N(q – 1) + 1} in such a way that (i) φ is 1–1 (ii) φ induces a bijection φ ...
V. Ramachandran
semanticscholar   +1 more source

ODD GRACEFUL LABELINGS OF GRAPHS

Discrete Mathematics, Algorithms and Applications, 2009
A graph G = (V(G), E(G)) with q edges is said to be odd graceful if there exists an injection f from V(G) to {0, 1, 2, …, 2q - 1} such that the edge labeling set is {1, 3, 5, …, 2q - 1} with each edge xy assigned the label |f(x) - f(y)|. In this paper, we prove that Pn × Pm (m = 2, 3, 4), generalized crown graphs Cn ⊙ K1,t and gear graphs are odd ...
Gao, Zhen-Bin, Zhang, Xiao-Dong, Xu, Li-Juan   +2 more
openaire   +1 more source