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Graceful and Antimagic Labelings
2019This chapter explores the relationship between antimagic labeling and alpha labelings and also the well-known graceful labelings. Much of this chapter looks at interesting labelings and structures on trees, including edge antimagic trees, alpha trees, and disjoint union of caterpillars.
Martin Bača +3 more
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Ordered Graceful Labellings of the 2-Star
Discrete Mathematics, 2001 The authors investigate ordered graceful labellings of 2-stars. They give a lower bound on the number of non-equivalent ordered graceful labellings by constructing an exponential number of such labellings. This shows that a conjecture of Cahit is false.
Richard J. Nowakowski +1 more
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The Generation of k-Graceful Figure and Graceful Label
2014 Fourth International Conference on Instrumentation and Measurement, Computer, Communication and Control, 2014This paper introduces the concept of graceful figure, discusses a special kind of graceful figure: K-graceful figure, draw all the graceful figure of the generated by the n side of all the beautiful label generation algorithm. The algebraic theory and computer tools introduced a graceful figure.
Jia Peipei, Zhang Tai, Zhang Yuanyuan
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On Graceful Labelings of Trees
2011A tree is a connected acyclic graph. A tree of n vertices is said to be graceful if the vertices can be assigned the labels {0, 1, 2, ..., n - 1} such that the absolute value of the differences in vertex labels between neighboring vertices generate the set consisting distinct values {1, 2, 3, ...,n-1}.
Sourabh Aryabhatta +3 more
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Graceful Labelings of Nearly Complete Graphs
Results in Mathematics, 2002A graph with \(q\) edges is graceful, if we can assign to each vertex an integer in \(\{0, 1, \ldots, q\}\), such that all edges have a different value of the absolute difference of the labels of its endpoints. This paper investigates which graphs that are `nearly complete', or a complete multipartite graph, are graceful.
Beutner, Detlev, Harborth, Heiko
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Graceful labeling based En (Grace) cryption and De (Grace) cryption
2013 IEEE International Conference ON Emerging Trends in Computing, Communication and Nanotechnology (ICECCN), 2013In recent years, Encryption has fascinated extra responsiveness owing to the swift development in multimedia and network technologies where the data has to be shielded from unauthorized access. Image scrambling scheme provide protection for digital images.
P. Mithun, N. R. Raajan
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On graceful and cordial labeling of shell graphs.
Ars Comb., 2011A graceful labeling, an \(\alpha \)-labeling (called here \(\Delta \)-labeling), and a cordial labeling of yet another special class of graphs are provided. Unfortunately, the paper contains many typographical, grammatical and stylistic errors.
G. Sethuraman 0001, K. Sankar
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A Metaheuristic Approach to the Graceful Labeling Problem
International Journal of Applied Metaheuristic Computing, 2010In graph theory, a graceful labeling of a graph G = (V, E) with n vertices and m edges is a labeling of its vertices with distinct integers between 0 and m inclusive, such that each edge is uniquely identified by the absolute difference between its endpoints.
Houra Mahmoudzadeh, Kourosh Eshghi
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Evolving labelings of graceful graphs
Proceedings of the Genetic and Evolutionary Computation Conference, 2022Luke Branson, Andrew M. Sutton
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