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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
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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
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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
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Line-graphs of cubic graphs are normal [PDF]
Discrete Mathematics, 2007 16 pages, 10 ...
Zsolt Patakfalvi
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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
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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.
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On pancyclic line graphs [PDF]
Czechoslovak Mathematical Journal, 1978 Ladislav Nebeský
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New results and open problems in line graphs
AKCE International Journal of Graphs and Combinatorics, 2022 Given a graph G with at least one edge, the line graph L(G) is that graph whose vertices are the edges of G, with two of these vertices being adjacent if the corresponding edges are adjacent in G.
Jay Bagga, Lowell Beineke
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Graph schema and best graph type to compare discrete groups: Bar, line, and pie
Frontiers in Psychology, 2022 Different graph types may differ in their suitability to support group comparisons, due to the underlying graph schemas. This study examined whether graph schemas are based on perceptual features (i.e., each graph type, e.g., bar or line graph, has its ...
Fang Zhao, Robert Gaschler
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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.
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