Results 41 to 50 of about 63,549 (264)
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On the in–out–proper orientations of graphs [PDF]
An orientation of a graph $G$ is {\it in-out-proper} if any two adjacent vertices have different in-out-degrees, where the in-out-degree of each vertex is equal to the in-degree minus the out-degree of that vertex. The {\it in-out-proper orientation number} of a graph $G$, denoted by $\overleftrightarrowχ(G)$, is $ \min_{D\in Γ}\max_{v\in V(G)} |d_D ...
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Research and Application of Hypernetwork Energy
Graph energy plays an important role in research of graph theory. Graph energy and many other similar variants have been applied in many other types of graphs, e.g., undirected graphs, oriented graphs, mixed graphs, and so on.
LIU Shengjiu, LI Tianrui, LIU Jia, XIE Peng
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An Orientation Theorem for Graphs
We characterize the class of graphs in which the edges can be oriented in such a way that going along any circuit in the graph, the number of forward edges minus the number of backward edges is equal to 0, 1, or \(- 1\). The result follows by applying Tutte's characterization of regular matroids to a certain binary matroid associated to a graph.
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Heroes in Orientations of Chordal Graphs
We characterize all digraphs $H$ such that orientations of chordal graphs with no induced copy of $H$ have bounded dichromatic number.
Pierre Aboulker +2 more
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From mice to humans—divergent strategies for intestinal homeostasis and regeneration
Recent advances such as organoid genome editing, xenotransplantation, imaging, and whole‐genome sequencing have enabled direct studies of human intestinal stem cells (ISCs). These studies reveal species‐specific features, including slower ISC proliferation, distinct injury responses, slower somatic mutation accumulation in humans, and an inverse ...
Keiko Ishikawa +2 more
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Skew-spectra and skew energy of various products of graphs [PDF]
Given a graph $G$, let $G^sigma$ be an oriented graph of $G$ with the orientation $sigma$ and skew-adjacency matrix $S(G^sigma)$. Then the spectrum of $S(G^sigma)$ consisting of all the eigenvalues of $S(G^sigma)$ is called the skew-spectrum of $G ...
Xueliang Li, Huishu Lian
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Notes on Knaster-Tarski Theorem versus Monotone Nonexpansive Mappings
The purpose of this note is to discuss the recent paper of Espínola and Wiśnicki about the fixed point theory of monotone nonexpansive mappings. In their work, it is claimed that most of the fixed point results of this class of mappings boil down to the ...
Khamsi Mohamed Amine
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Interpreting the effects of DNA polymerase variants at the structural level
Using MAVISp and molecular dynamics simulations, we analyzed over 60 000 missense variants in POLE and POLD1 from ClinVar, COSMIC, cBioPortal, and saturation mutagenesis. Identified mechanistic indicators, including stability, binding, and long‐range, enable structural interpretation, providing ACMG‐like evidence for possible reclassification of VUS ...
Matteo Arnaudi +7 more
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An Overview of Knowledge Graph Reasoning: Key Technologies and Applications
In recent years, with the rapid development of Internet technology and applications, the scale of Internet data has exploded, which contains a significant amount of valuable knowledge.
Yonghong Chen +6 more
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