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Graceful Labelings of Pendant Graphs [PDF]
, 2017 In 1967, Alexander Rosa introduced a new type of graph labeling called a graceful labeling. This paper will provide some background on graceful labelings and their relation to certain types of graphs called pendant graphs.
Graf, Alessandra
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Advanced Science, EarlyView.Unlocking new reactivity: a palladium‐catalyzed coupling of gem‐iododiborylalkanes with electron‐rich olefins enables streamlined access to β,β‐diboryl carbonyl compounds under mild conditions. Mechanistic insights reveal a Pd(0)/Pd(I) cycle and a diboryl‐stabilized radical intermediate, offering a distinct platform for advancing unconventional ...
Xiao‐Yu Xie +4 more
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Octagonal prime graceful labeling
Ratio MathematicaLet G be a graph with p vertices and q edges. Define a bijection f : V (G) → {1, 8, ..., p(3p - 2)} by f(vi) = i(3i - 2) for every i from 1 to p and define a 1 - 1 mapping fopgl ∗ : E(G) → set of natural number N such that f∗(uv) = |f(u) - f(v)| for all ...
V Akshaya
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Alpha labelings of full hexagonal caterpillars
AKCE International Journal of Graphs and Combinatorics, 2016 Barrientos and Minion (2015) introduced the notion of generalized snake polyomino graphs and proved that when the cells are either squares or hexagons, then they admit an alpha labeling. Froncek et al.
Dalibor Froncek
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AKCE International Journal of Graphs and Combinatorics, 2020 When a graceful labeling of a bipartite graph assigns the smaller labels to the vertices of one of the stable sets of the graph, the assignment is called an α-labeling. Any graph that admits such a labeling is an α-graph.
Christian Barrientos, Sarah Minion
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Graceful labelling of the union of paths and cycles
Discrete Mathematics, 1999 Frucht and Salinas (Ars. Combin. 20 (1985) 143–157) have proved that C4∪Pn is graceful, for every n⩾3, and they have conjectured that Cs∪Pn is graceful if n+s⩾7. In this paper we show that Cs∪Pn is graceful if s⩾5 and n⩾(s+5)/2.
Sheshayya A. Choudum +1 more
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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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Artificial Internalizing Receptors for Targeted Degradation of Extracellular Proteins
Advanced Science, EarlyView.Small organic molecules that are anchored into the lipid bilayer of a mammalian cell and have an exofacial recognition ligand can act as artificial internalizing receptors. These receptors are an efficacious tool to selectively capture and internalize cognate antibodies from the extracellular environment in a protein‐specific manner.
Ane B. Søgaard +3 more
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The Graceful Coalescence of Alpha Cycles
Communications in Advanced Mathematical Sciences, 2019 The standard coalescence of two graphs is extended, allowing to identify two isomorphic subgraphs instead of a single vertex. It is proven here that any succesive coalescence of cycles of size $n$, where $n$ is divisible by four, results in an $\alpha ...
Christian Barrientos, Sarah Minion
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On alpha labeling of tensor product of paths and cycles. [PDF]
Heliyon, 2023 L U, G R.
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