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On hamiltonian line-graphs [PDF]
Introduction. The line-graph L(G) of a nonempty graph G is the graph whose point set can be put in one-to-one correspondence with the line set of G in such a way that two points of L(G) are adjacent if and only if the corresponding lines of G are adjacent.
Gary Chartrand
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Word-Representability of Line Graphs [PDF]
10 pages, 5 ...
Kitaev, Sergey+3 more
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TransLiG: a de novo transcriptome assembler that uses line graph iteration. [PDF]
We present TransLiG, a new de novo transcriptome assembler, which is able to integrate the sequence depth and pair-end information into the assembling procedure by phasing paths and iteratively constructing line graphs starting from splicing graphs ...
Liu J, Yu T, Mu Z, Li G.
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On line-symmetric graphs [PDF]
An edge automorphism \(\lambda\) of a nonempty graph G is called induced if there is a vertex automorphism \(\alpha\) of G such that \(\lambda (e)=\alpha (x)\alpha (y)\) for each edge \(e=xy\) of G. A nonempty graph G is line-symmetric if for all edges e and f of G there is some induced edge automorphism \(\lambda\) for which \(\lambda (e)=f.\) The ...
David Burns+2 more
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Every $3$-connected, essentially $11$-connected line graph is hamiltonian [PDF]
Thomassen conjectured that every $4$-connected line graph is hamiltonian. A vertex cut $X$ of $G$ is essential if $G-X$ has at least two nontrivial components. We prove that every $3$-connected, essentially $11$-connected line graph is hamiltonian. Using
Hong-Jian Lai+3 more
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Line-graphs of cubic graphs are normal [PDF]
16 pages, 10 ...
Zsolt Patakfalvi
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On pancyclic line graphs [PDF]
Ladislav Nebeský
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Clique-transversal sets of line graphs and complements of line graphs
AbstractA clique-transversal set T of a graph G is a set of vertices of G such that T meets all maximal cliques of G. The clique-transversal number, denoted τc(G), is the minimum cardinality of a clique-transversal set. Let n be the number of vertices of G. We study classes of graphs G for which n2 is an upper bound for τc(G).
Thomas Andreae+2 more
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Atomistic Line Graph Neural Network for improved materials property predictions [PDF]
Graph neural networks (GNN) have been shown to provide substantial performance improvements for atomistic material representation and modeling compared with descriptor-based machine learning models.
K. Choudhary, Brian L. DeCost
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LGESQL: Line Graph Enhanced Text-to-SQL Model with Mixed Local and Non-Local Relations [PDF]
This work aims to tackle the challenging heterogeneous graph encoding problem in the text-to-SQL task. Previous methods are typically node-centric and merely utilize different weight matrices to parameterize edge types, which 1) ignore the rich semantics
Ruisheng Cao+5 more
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