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Line Graph Links

Acta Mathematicae Applicatae Sinica, English Series, 2021
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Yang, Wei-ling   +2 more
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Iteratedk-line graphs

Graphs and Combinatorics, 1994
``For integers \(k \geq 2\), the \(k\)-line graph of a graph \(G\) is defined as a graph whose vertices correspond to the complete subgraphs on \(k\) vertices in \(G\) with two distinct vertices adjacent if the corresponding complete subgraphs have \(k-1\) common vertices in \(G\).'' Starting with a graph \(G\), one can construct the sequence of graphs
Le Van Bang, Prisner, Erich
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On Traceable Line Graphs

Graphs and Combinatorics, 2013
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Niu, Zhaohong, Xiong, Liming
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Line Graphs of Signed Graphs

2021
Signed graphs are another interesting variation of graphs, usually taken to be graphs in which each edge is either positive or negative. In the literature, there is more than one option for the rule for the labels on the edges of the line graph, and two of these will be considered here.
Lowell W. Beineke, Jay S. Bagga
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Uniquely Line Colorable Graphs

Canadian Mathematical Bulletin, 1973
A line-coloring of a graph G is an assignment of colors to the lines of G so that adjacent lines are colored differently; an n-line coloring uses n colors. The line-chromatic number χ'(G) is the smallest n for which G admits an n-line coloring.
Greenwell, D. L., Kronk, H. V.
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Collapsible Graphs and Hamiltonicity of Line Graphs

Graphs and Combinatorics, 2013
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Yang, Weihua   +3 more
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Supereulerian line graphs

Discrete Mathematics, 2022
A connected graph is said to be supereulerian if it containes a spanning Eulerian subgraph. The interest in these graphs comes from the fact that such a graph has a Hamiltonian line graph. A graph \(G\) is called essentially \(k\)-edge connected if \(G\) does not have an essential edge cut \(X\) with \(|X| < k.\) The main results of this paper ...
Shangguan, Yingmin, Xiong, Liming
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Neighbourhood-Perfect Line Graphs

Graphs and Combinatorics, 1994
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