Results 11 to 20 of about 5,414,210 (302)
On chordal graph and line graph squares [PDF]
Discrete Applied Mathematics, 2018 In this work we investigate the chordality of squares and line graph squares of graphs. We prove a sufficient condition for the chordality of squares of graphs not containing induced cycles of length at least five. Moreover, we characterize the chordality of graph squares by forbidden subgraphs.
Robert Scheidweiler +1 more
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Treewidth of the Line Graph of a Complete Graph [PDF]
Journal of Graph Theory, 2014 AbstractIn recent articles by Grohe and Marx, the treewidth of the line graph of a complete graph is a critical example—in a certain sense, every graph with large treewidth “contains” . However, the treewidth of was not determined exactly. We determine the exact treewidth of the line graph of a complete graph.
Daniel J. Harvey, David R. Wood
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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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A number theoretic problem on super line graphs
AKCE International Journal of Graphs and Combinatorics, 2016 In Bagga et al. (1995) a generalization of the line graph concept was introduced. Given a graph G with at least r edges, the super line graph of index r, Lr(G), has as its vertices the sets of r edges of G, with two adjacent if there is an edge in one ...
Jay Bagga, Lowell Beineke, Badri Varma
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Tulgeity of Line, Middle and Total Graph of Wheel Graph Families [PDF]
, 2010 Tulgeity r(G) is the maximum number of disjoint, point induced, non acyclic subgraphs contained in G. In this paper one finds the tulgeity of line, middle and total graph of wheel graph, Gear graph and Helm ...
Vernold, Vivin +2 more
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Solutions of Detour Distance Graph Equations
Sensors, 2022 Graph theory is a useful mathematical structure used to model pairwise relations between sensor nodes in wireless sensor networks. Graph equations are nothing but equations in which the unknown factors are graphs.
S. Celine Prabha +7 more
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On the Representability of Line Graphs [PDF]
, 2011 10 pages, 5 ...
Sergey Kitaev +3 more
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On the Planarity of Generalized Line Graphs
Theory and Applications of Graphs, 2019 One of the most familiar derived graphs is the line graph. The line graph $L(G)$ of a graph $G$ is that graph whose vertices are the edges of $G$ where two vertices of $L(G)$ are adjacent if the corresponding edges are adjacent in~$G$.
Khawlah H. Alhulwah +2 more
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Under which conditions is λ″(G)=κ″(L(G))?
AKCE International Journal of Graphs and Combinatorics, 2023 In this paper we show that if G is a connected graph such that [Formula: see text], [Formula: see text] and [Formula: see text] then [Formula: see text] exists and [Formula: see text] if and only if G is not super-[Formula: see text]. We also obtain some
Farnaz Soliemany +2 more
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Journal of Combinatorial Theory, Series B, 2018 The treewidth of a graph is an important invariant in structural and algorithmic graph theory. This paper studies the treewidth of line graphs. We show that determining the treewidth of the line graph of a graph $G$ is equivalent to determining the minimum vertex congestion of an embedding of $G$ into a tree.
Daniel J. Harvey, David R. Wood
openaire +2 more sources