Results 81 to 90 of about 29,089 (268)
On the Planarity of Generalized Line Graphs
Theory and Applications of Graphs, 2019 One of the most familiar derived graphs is the line graph. The line graph $L(G)$ of a graph $G$ is that graph whose vertices are the edges of $G$ where two vertices of $L(G)$ are adjacent if the corresponding edges are adjacent in~$G$.
Khawlah H. Alhulwah +2 more
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On the planarity of jump graphs
Discrete Mathematics, 2000 Let \(G\) be a graph of size \(m\geq 1\) and let \(F\) and \(H\) be edge-induced subgraphs of \(G\) of size \(k\) with \(1\leq k\leq m\). In the literature is then defined the \(k\)-jump distance from \(F\) to \(H\). For a graph \(G\) of size \(m\geq 1\) and an integer \(k\) with \(1\leq k\leq m\), the \(k\)-jump graph \(J_k(G)\) is defined as a graph ...
Héctor Hevia +2 more
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Advanced Functional Materials, EarlyView.ABSTRACT Traditional wearable exoskeletons rely on rigid structures, which limit comfort, flexibility, and everyday usability. This work introduces the fundamental technologies to create the first soft, lightweight, intelligent textile‐based exoskeletons (Texoskeletons) built using 1D sensors and actuators.
Amy Lukomiak +19 more
wiley +1 more source
CoRR, 2018 We show that for any $k \geq 0$, there exists a planar graph which is $B_{k+1}$-CPG but not $B_k$-CPG. As a consequence, we obtain that $B_k$-CPG is a strict subclass of $B_{k+1}$-CPG.
Nicolas Champseix +2 more
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Advanced Functional Materials, EarlyView.Field‐free spin‐orbit torque domain‐wall synapses integrated with stochastic MTJ neurons enable compact hardware Boltzmann machines. Leveraging intrinsic stochasticity and multi‐level conductance, the system achieves efficient probabilistic learning with high accuracy, demonstrating a scalable spintronic platform for energy‐efficient edge AI.
Aijaz H. Lone +8 more
wiley +1 more source
2-distance 4-coloring of planar subcubic graphs with girth at least 21 [PDF]
Discrete Mathematics & Theoretical Computer ScienceA $2$-distance $k$-coloring of a graph is a proper vertex $k$-coloring where vertices at distance at most 2 cannot share the same color. We prove the existence of a $2$-distance $4$-coloring for planar subcubic graphs with girth at least 21. We also show
Hoang La, Mickael Montassier
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Structure‐Guided Dynamical Mechanics in Bioinspired Double Twisted Laminated Thin Films
Advanced Functional Materials, EarlyView.This work explores a dynamic mechanistic study of crack propagation and puncture testing via real‐time monitoring of crack initiation, propagation, and termination through nature‐inspired single and double twisted architectures fabricated from cellulose nanocrystals.
Justin Brackenridge +4 more
wiley +1 more source
Decomposing a Planar Graph into Degenerate Graphs
Journal of Combinatorial Theory, Series B, 1995 A graph \(G\) is \(k\)-degenerate if every subgraph of \(G\) has a vertex of degree less than \(k\). The author proves that the vertex set of any planar graph can be decomposed into two sets such that one of them induces a 3-degenerate graph and the other induces a 2-degenerate graph.
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Electronic Notes in Discrete Mathematics, 2001 Abstract Abstract We generalize the idea of extended triangles of a graph G by considering a family of completes of G instead of the clique family of G. We characterize Helly and 3 - Helly Planar Graphs using extended triangles. We prove that if a planar graph is a clique graph then any one of its extended triangles is a clique graph.
Liliana Alcón, Marisa Gutierrez
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Advanced Functional Materials, EarlyView.Engineering MnNiPx cathodes through the dual role of Mn simultaneously improves hydrogen evolution reaction activity and intermittent‐operation durability. Mn preferentially oxidizes to protect Ni–P sites from irreversible oxidation, while metallic Mn incorporation enhances the HER kinetics of Ni–P active layer.
Ik‐Sun Kim +16 more
wiley +1 more source