Results 41 to 50 of about 828 (253)
GRACEFUL CHROMATIC NUMBER OF SOME CARTESIAN PRODUCT GRAPHS
Ural Mathematical Journal, 2023 A graph \(G(V,E)\) is a system consisting of a finite non empty set of vertices \(V(G)\) and a set of edges \(E(G)\). A (proper) vertex colouring of \(G\) is a function \(f:V(G)\rightarrow \{1,2,\ldots,k\},\) for some positive integer \(k\) such that ...
I Nengah Suparta +3 more
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Discrete Mathematics, 1980 AbstractIn this paper, we prove that the n-cube is graceful, thus answering a conjecture of J.-C. Bermond and Gangopadhyay and Rao Hebbare. To do that, we introduce a special kind of graceful numbering, particular case of α-valuation, called strongly graceful and we prove that if a graph G is strongly graceful, G + K2 is also strongly graceful.
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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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Edge odd graceful labeling of some path and cycle related graphs
AKCE International Journal of Graphs and Combinatorics, 2017 Solairaju and Chithra introduced a new type of labeling of a graph with vertices and edges called an edge odd graceful labeling if there is a bijection from the edges of the graph to the set such that, when each vertex is assigned the sum of all edges ...
S.N. Daoud
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A New Measure for Gracefulness of Graphs
Electronic Notes in Discrete Mathematics, 2015 Abstract Let G = ( V , E ) be a ( p , q ) -graph without isolated vertices. The gracefulness grac ( G ) of G is the smallest positive integer k for which there exists an injective function f : V → { 0 , 1 , 2 , … , k } such that the edge induced function g f : E → { 1 , 2 ...
Jessica Pereira +2 more
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Evaluating the involvement of autolysosomes in the nuclear translocation of fluorescent proteins
FEBS Open Bio, EarlyView.Endogenously expressed fluorescent proteins can be degraded by autophagy and transported to cell nuclei via the nuclear pore complex. But in some cell lines, for example, HeLa cells which are positive for immunoreactivity of a receptor ligand, such as UCN I, in cell nuclei, fusion of autolysosome with the nuclear envelope is involved in the nuclear ...
Keiichi Ikeda
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PASTA‐ELN: Simplifying Research Data Management for Experimental Materials Science
Advanced Engineering Materials, EarlyView.Research data management faces ongoing hurdles as many ELNs remain complex and restrictive. PASTA‐ELN offers an open‐source, cross‐platform solution that prioritizes simplicity, offline access, and user control. Its in tuitive folder structure, modular Python add‐ons, and open formats enable seamless documentation, FAIR data practices, and easy ...
S. Brinckmann, G. Winkens, R. Schwaiger
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International Journal of Mathematics and Mathematical Sciences, 2002 We construct a labeled graph D(n) that reflects the structure of divisors of a given natural number n. We define the concept of graceful numbers in terms of this associated graph and find the general form of such a number.
Kiran R. Bhutani, Alexander B. Levin
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Adaptive Foam 3D Printing of Ultralight and Multifunctional Materials
Advanced Engineering Materials, EarlyView.Adaptive foam 3D printing, enabled by expandable microspheres, imparts cellular structures to thermoplastic and thermosetting polymers, manufactured through a variety of processes including fused filament fabrication, direct ink writing, digital light processing, and inkjet printing.
Nariman Rajabifar, Amir Ameli
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Advanced Materials, EarlyView.Spatiotemporal control over cell behavior within bioprinted constructs remains a key challenge in biofabrication. Volumetric bioprinting using multi‐wavelength light sources permits to activate light‐sensitive intracellular proteins as well as optogenetic gene and protein expression circuits in bioprinted cells, in addition to enabling fast printing of
Davide Ribezzi +14 more
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