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Line graph characterization of power graphs of finite nilpotent groups [PDF]
Communications in Algebra, 2022, 2021 This paper deals with the classification of groups $G$ such that power graphs and proper power graphs of $G$ are line graphs. In fact, we classify all finite nilpotent groups whose power graphs are line graphs. Also, we categorize all finite nilpotent groups (except non-abelian $2$-groups) whose proper power graphs are line graphs.
S. Bera
arxiv +3 more sources
On hamiltonian line-graphs [PDF]
Transactions of the American Mathematical Society, 1968 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
openalex +3 more sources
TransLiG: a de novo transcriptome assembler that uses line graph iteration. [PDF]
Genome Biol, 2019 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.
europepmc +2 more sources
Graphs whose line graphs are ring graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 Given a graph H, a path of length at least two is called an H-path if meets H exactly in its ends. A graph G is a ring graph if each block of G which is not a bridge or a vertex can be constructed inductively by starting from a single cycle and then in ...
Mahdi Reza Khorsandi
doaj +3 more sources
Every $3$-connected, essentially $11$-connected line graph is hamiltonian [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 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
doaj +3 more sources
Line-graphs of cubic graphs are normal [PDF]
Discrete Mathematics, 2007 16 pages, 10 ...
Zsolt Patakfalvi
openalex +5 more sources
Clique-transversal sets of line graphs and complements of line graphs
Discrete Mathematics, 1991 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
openalex +3 more sources
On Bivariegated Graphs and Line Graphs [PDF]
arXiv, 2018 This note is on the structures of line graphs and 2-variegated graphs. We have given here solutions of some graph equations involving line graphs and 2-variegated graphs. In addition, a characterization of potentially 2-variegated line graphic degree sequences is given.
arxiv +3 more sources
On pancyclic line graphs [PDF]
Czechoslovak Mathematical Journal, 1978 Ladislav Nebeský
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Atomistic Line Graph Neural Network for improved materials property predictions [PDF]
npj Computational Materials, 2021 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
semanticscholar +1 more source