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In this article, we adapt the edge-graceful graph labeling definition into block designs and define a block design V,B with V=v and B=b as block-graceful if there exists a bijection f:B⟶1,2,…,b such that the induced mapping f+:V⟶Zv given by f+x=∑x∈AA ...
Dilara Erdemir, Emre Kolotoğlu
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Super total graceful labeling of some trees
A graph labeling is an assignment of integers to the edges, vertices, or both of a graph so that it meets to certain conditions. A graph labeling is called total labeling if labeling is given to edges and vertices.
I. N. Khasanah, Purwanto
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Most in vitro cancer models lack cellular diversity, functional complexity, and clinical relevance. This work highlights the generation of an innovative dynamic tetraculture with autologous patient‐derived cells within a vascularized tumor‐on‐chip, as well as the recapitulation of endothelial anergy features induced by the tumor microenvironment ...
Christine Lansche+16 more
wiley +1 more source
Pelabelan Graceful Sisi-ganjil Pada Graf Web W(2,n) [PDF]
Let G = (V(G),E()) be a graph with vertex set () and edge set (). Assume that graph G have edge. Graceful edge-odd labeling is a bijective map ∶ () → {1, 3, 5,…,2 – 1} that resulting map + : () → {0,1,2,…,2 −1} with
Djuwandi, D. (Djuwandi)+2 more
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On Cubic Graceful Labeling [PDF]
A graph with n vertex and m edges is said to be cubic graceful labeling if its vertices are labeled with distinct integers {0,1,2,3,……..,m3} such that for each edge f*( uv) induces edge mappings are {13,23,33,……,m3}.
, Mathew Varkey T. K, Mini. S. Thomas
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Edge even graceful labeling of some corona graphs
Elsonbaty and Daoud introduced a labeling of graph with p vertices and q edges called edge even graceful labeling i.e. a bijective function f of the edge set E(G) into the set {2,4,6, . . . , 2q} such that the induced function f*:V(G) → {0,2,4, . . ., 2k
D. Jayantara, Purwanto, S. Irawati
semanticscholar +1 more source
Thermoresponsive BrushGel Microcarriers for Efficient Cell Expansion and Enzyme‐Reduced Harvesting
Askari et al, report on temperature‐responsive microcarriers to minimize enzyme use and cost in dynamic cultures. Abstract Scaling up cell therapy requires efficient expansion of high‐quality cells. Microcarrier(MC)‐based systems offer high surface‐to‐volume ratios and reduce culture media usage.
Esfandyar Askari+9 more
wiley +1 more source
On Graceful Spider Graphs with at Most Four Legs of Lengths Greater than One
A graceful labeling of a tree T with n edges is a bijection f:V(T)→{0,1,2,…,n} such that {|f(u)-f(v)|:uv∈E(T)} equal to {1,2,…,n}. A spider graph is a tree with at most one vertex of degree greater than 2. We show that all spider graphs with at most four
A. Panpa, T. Poomsa-ard
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On graphs with α- and b-edge consecutive edge magic labelings
Among the most studied graph labelings we have the varieties called alpha and edge-magic. Even when their definitions seem completely different, these labelings are related.
Christian Barrientos
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Graceful Labeling Algorithms and Complexity – a Survey [PDF]
Graceful graphs were first studied by Rosa in 1966. The Kotzig-Ringel graceful tree conjecture states that every tree has a graceful labeling. Aldred and McKay and others have used computer programs to show that trees of order up to 35 are graceful ...
Arumugam, S. (S), Bagga, J. (Jay)
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