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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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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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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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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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Graceful labeling for mushroom trees
Aequationes mathematicae, 2014A graceful labelling of a graph \(G=(V(G),E(G))\) on \(n\) vertices is a mapping \(f:V(G)\rightarrow \{0,1,\dots,n\}\) such that the mapping with \(\{x,y\}\mapsto |f(x)-f(y)|\) is injective on the set of edges of \( G\). The authors prove that if \(T\) is a tree of order \(k+1\) and \(S\) is a star with at least \((e^{4/e})^k\) leaves then any graph ...
Cheung, WS, Ng, TW, Chan, TL
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Graceful Labelings: The Shifting Technique
2017Graceful labelings of graphs appeared in 1967 due to the relationship found with the problem of decompositions of graphs, in particular with the problem of decomposing complete graphs into copies of a given tree. Strong relations between graceful labelings and Golomb rulers (which are a different way to understand Sidon sets) were also found.
Susana C. López +1 more
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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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Real-graceful labellings: a generalisation of graceful labellings
2011Every graph can be associated to a characteristic exponential equation involving powers of (say) 2, whose unknowns represent vertex labels and whose general solution is equivalent to a graceful labelling of the graph. If we do not require that the solutions be integers, we obtain a generalisation of a graceful labelling that uses real numbers as labels.
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