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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 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 +8 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
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
Characterization of Line-Consistent Signed Graphs
Discussiones Mathematicae Graph Theory, 2015 The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent signed graphs, i.e.
Slilaty Daniel C., Zaslavsky Thomas
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
On the hardness of recognizing triangular line graphs [PDF]
arXiv, 2010 Given a graph G, its triangular line graph is the graph T(G) with vertex set consisting of the edges of G and adjacencies between edges that are incident in G as well as being within a common triangle. Graphs with a representation as the triangular line graph of some graph G are triangular line graphs, which have been studied under many names including
Anand, Pranav +4 more
arxiv +7 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