Results 31 to 40 of about 836 (298)
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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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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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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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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Advanced Functional Materials, EarlyView.This study demonstrates that the dual delivery of BMP‐2/‐7 coding cmRNAs for bone healing is demonstrated as feasible, safe, and highly osteogenic. Compared to single BMP‐2 or BMP‐7 cmRNAs, the combination enhances the production of both mineral and organic components of the extracellular matrix when delivered using a collagen‐HA scaffold, supporting ...
Claudia Del Toro Runzer +7 more
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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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Advanced Functional Materials, EarlyView.This review explores functional and responsive materials for triboelectric nanogenerators (TENGs) in sustainable smart agriculture. It examines how particulate contamination and dirt affect charge transfer and efficiency. Environmental challenges and strategies to enhance durability and responsiveness are outlined, including active functional layers ...
Rafael R. A. Silva +9 more
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Graceful labeling of hexagonal snakes [PDF]
AIP Conference Proceedings, 2019 Consider a graph G with p number of vertices and q number of edges. If the edges of the graph are labeled by subtracting the corresponding vertex label of the respective edges following the condition that the labels of the vertices and edges are distinct is known as Graceful labeling of a graph.
Lalitha Pattabiraman +2 more
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Advanced Functional Materials, EarlyView.A 3D disease model is developed using customized hyaluronic‐acid‐based hydrogels supplemented with extracellular matrix (ECM) proteins resembling brain ECM properties. Neurons, astrocytes, and tumor cells are used to mimic the native brain surrounding.
Esra Türker +16 more
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