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Odd Harmonious Labeling of Some Graphs [PDF]
, 2012 The labeling of discrete structures is a potential area of research due to its wide range of applications.
Shah, N.H., Vaidya, S.K.
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Radio Heronian Mean k-Graceful Labeling on Degree Splitting of Graphs
Ratio Mathematica, 2023 A mapping g:V\left(G\right)\rightarrow{k,k+1,\ldots,k+N-1} is a radio heronian mean k-labeling such that if for any two distinct vertices s and t of G, d\left(s,t\right)+\left\lceil\frac{g\left(s\right)+g\left(t\right)+\sqrt{g\left(s\right)g\left(t\right)
K Sunitha, K Vimal Rani
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Applications of mathematical programming in graceful labeling of graphs
Journal of Applied Mathematics, 2004 Graceful labeling is one of the best known labeling methods of graphs. Despite the large number of papers published on the subject of graph labeling, there are few particular techniques to be used by researchers to gracefully label graphs. In this paper,
Kourosh Eshghi, Parham Azimi
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One curious identity counting graceful labelings
Enumerative Combinatorics and Applications, 2021 Let $a$ and $b$ be positive integers with prime factorisations $a = p_1^np_2^n$ and $b = q_1^nq_2^n$. We prove that the number of essentially distinct $α$-graceful labelings of the complete bipartite graph $K_{a, b}$ equals the alternating sum of fourth powers of binomial coefficients $(-1)^n[\binom{2n}{0}^4 - \binom{2n}{1}^4 + \binom{2n}{2}^4 - \binom{
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Lucas Gracefulness of Almost and Nearly for Some Graphs [PDF]
, 2011 By a graph, we mean a finite undirected graph without loops or multiple ...
Nagarajan, A. +2 more
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Graceful And Graceful Labeling Of Graphs
, 2018 {"references": ["1.\tJ. A. Gallian, A Dynamic survey of graph labeling, The electronic journal of combinatory 16 (2009).DS6. 2.\tI. Gutman, The energy of a graph, Ber. Math-satist. sekt. Forschungsz. Graz 103 (1978), 1-22. 3.\tGutman and B. Zhou, Laplacian energy of a graph, linear algebra appl. 414 (2006), 29-37. 4.\tI.
M. Soundharya, R. Balakumar
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Electronic Journal of Graph Theory and Applications, 2020 Two methods for expanding graceful trees are introduced. In constructing a larger graceful trees, these methods are based on a collection of certain graceful trees and one graceful tree as the core of the produced graceful tree.
I Nengah Suparta, I Dewa M. Agus Ariawan
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Discussiones Mathematicae Graph Theory, 2016 For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G).
Niedzialomski Amanda
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Special Graceful Labelings of Irregular Fences and Lobsters
Universal Journal of Mathematics and Applications, 2019 Irregular fences are subgraphs of $P_m \times P_n$ formed with $m$ copies of $P_n$ in such a way that two consecutive copies of $P_n$ are connected with one or two edges; if two edges are used, then they are located in levels separated an odd number of ...
Christian Barrientos
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Advanced Functional Materials, EarlyView.A transparent, laser‐microscribed glass platform enables cancer diagnosis within 1 h—much faster than histology, which takes days, and free from the chemical or contrast risks of MRI or CT scans. The antibody‐functionalized rough glass surface captures viable cancer cells directly from suspension, allowing instant optical readout and offering a rapid ...
Anish Pal +5 more
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