Results 41 to 50 of about 617,805 (269)
BIPARTITE GRAPH ASSOCIATED WITH ELEMENTS AND COSETS OF SUBRINGS OF FINITE RINGS
Barekeng, 2023 Let be a finite ring. The bipartite graph associated to elements and cosets of subrings of is a simple undirected graph with vertex set , where is the set of all subrings of , and two vertices and are adjacent if and only if In this study, we ...
Hubbi Muhammad +3 more
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Evaluating the rank generating function of a graphic 2-polymatroid [PDF]
, 2006 We consider the complexity of the two-variable rank generating function, $S$, of a graphic 2-polymatroid. For a graph $G$, $S$ is the generating function for the number of subsets of edges of $G$ having a particular size and incident with a particular ...
Noble, SD, Noble, Steven
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Engineering Ferrimagnetic Interactions in Molecular Quantum Systems
Angewandte Chemie, EarlyView.Heterospin nanographene architectures—constructed by covalently linking spin‐1/2$\nicefrac {1}{2}$ and spin‐1 triangular units via on‐surface synthesis—are characterized by bond‐resolved scanning probe microscopy. Inelastic electron tunneling spectroscopy probes exchange interactions within a Heisenberg model, revealing both compensated (S=0$S=0$) and ...
Elia Turco +8 more
wiley +2 more sources
Electronic Notes in Discrete Mathematics, 1999 Two graphs \(G\) and \(H\) on the vertex set \(V\) are \(P_4\)-isomorphic if there is a permutation \(\pi\) on \(V\) such that, for all subsets \(S\) of \(V\), \(S\) induces a chordless \(P_4\) in \(G\) if and only if \(\pi (S)\) induces a \(P_4\) in \(H\). The author characterizes all graphs \(P_4\)-isomorphic to a bipartite graph. For example, we can
openaire +3 more sources
Bipartite dimensions and bipartite degrees of graphs
Discrete Mathematics, 1996 Let \(G=(V,E)\) be an undirected graph with finite nonempty vertex set \(V\) and irreflexive edge set \(E\). The irreflexive complement of \(G\) is denoted by \(G^c=(V,E^c)\) with \(E^c=\{\{u,v\}:u, v\in V, u\neq v, \{u,v\}\not\in E\}\). A cover of a graph \(G\) is a family of complete bipartite subgraphs of \(G\) whose edges cover the edges of \(G ...
Peter C. Fishburn, Peter L. Hammer
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In Vitro Selection of Functional Neoproteins Containing Highly Fluorinated Cores
Angewandte Chemie, EarlyView.The generation of neoproteins—functional proteins containing unnatural amino acids—is a key goal in synthetic biology. We develop a platform to discover neoproteins with specified bioactivity from trillion‐member sequence libraries, using genetic code reprogramming, in vitro selection and microwave peptide synthesis.
Adam Beattie +5 more
wiley +2 more sources
Bipartite Diametrical Graphs of Diameter 4 and Extreme Orders
International Journal of Mathematics and Mathematical Sciences, 2008 We provide a process to extend any bipartite diametrical graph of diameter 4 to an 𝑆-graph of the same diameter and partite sets. For a bipartite diametrical graph of diameter 4 and partite sets 𝑈 and 𝑊, where 2𝑚=|𝑈|≤|𝑊|, we prove that 2𝑚 is a sharp ...
Salah Al-Addasi, Hasan Al-Ezeh
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Decomposing dense bipartite graphs into 4-cycles [PDF]
, 2015 Let G be an even bipartite graph with partite sets X and Y such that |Y | is even and the minimum degree of a vertex in Y is at least 95|X|/96. Suppose furthermore that the number of edges in G is divisible by 4.
Nicholas J. Cavenagh +1 more
core
Packing four copies of a tree into a complete bipartite graph [PDF]
, 2022 summary:In considering packing three copies of a tree into a complete bipartite graph, H. Wang (2009) gives a conjecture: For each tree $T$ of order $n$ and each integer $k\geq 2$, there is a $k$-packing of $T$ in a complete bipartite graph $B_{n+k-1 ...
Pu, Liqun, Gao, Xiaoli, Tang, Yuan
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Advances in Applied Mathematics, 1999 Let \(R = K[t_1, \ldots , t_d]\) be the polynomial ring in \(d\) indeterminates over a field \(K\). If \(G\) is a bipartite graph on the vertex set \(\{ 1, \ldots , d \}\), define \(K[G]\) to be the subalgebra of \(R\) generated by all monomials \(t_i t_j\) such that \(\{ i,j \}\) is an edge of \(G\). It is shown that if every \(n\)-cycle \((n \geq 6)\)
Ohsugi, Hidefumi, Hibi, Takayuki
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