Results 1 to 10 of about 1,844,339 (310)
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
On the Representability of Line Graphs [PDF]
Open Journal of Discrete Mathematics, 2011 A graph G=(V,E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x,y) is in E for each x not equal to y.
Kitaev, Sergey +3 more
core +9 more sources
On line-symmetric graphs [PDF]
Fundamenta Mathematicae, 1984 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
openalex +4 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
openalex +3 more sources
Line-graphs of cubic graphs are normal [PDF]
Discrete Mathematics, 2007 16 pages, 10 ...
Zsolt Patakfalvi
openalex +4 more sources
On pancyclic line graphs [PDF]
Czechoslovak Mathematical Journal, 1978 Ladislav Nebeský
openalex +4 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
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
doaj +1 more source
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
doaj +1 more source
Independent point-set domination in line graphs
AKCE International Journal of Graphs and Combinatorics, 2021 Line graph of a graph G is an intersection graph of the edge set E(G) of G. In this paper, we obtain a sharp upper bound on the diameter of graph G whose line graph is an ipsd graph (graph possessing an independent point-set dominating set) by ...
Purnima Gupta, Alka Goyal, Ranjana Jain
doaj +1 more source