Results 51 to 60 of about 1,939,159 (235)
Discrete Mathematics, 2011 Boxicity of a graph H, denoted by box(H), is the minimum integer k such that H is an intersection graph of axis-parallel k-dimensional boxes in R^k. In this paper, we show that for a line graph G of a multigraph, box(G) <= 2 (\lceil log_2(log_2( )) \rceil + 3) + 1, where denotes the maximum degree of G. Since <= 2( - 1), for any line graph
Chandran, Sunil L +2 more
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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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On Hamilton Decompositions of Line Graphs of Non-Hamiltonian Graphs and Graphs without Separating Transitions [PDF]
, 2017 In contrast with Kotzig's result that the line graph of a $3$-regular graph $X$ is Hamilton decomposable if and only if $X$ is Hamiltonian, we show that for each integer $k\geq 4$ there exists a simple non-Hamiltonian $k$-regular graph whose line graph ...
Bryant, Darryn +2 more
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Graph Equation for Line Graphs and m-Step Graphs [PDF]
Graphs and Combinatorics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kim, Seog-Jin +4 more
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Line graph embedding of co-intersection graph of ideals of commutative rings
AKCE International Journal of Graphs and CombinatoricsThis research paper focuses on the co-intersection graph of a commutative ring [Formula: see text]. The co-intersection graph of [Formula: see text] denoted by [Formula: see text] is a simple graph with vertices that are non-trivial ideals of [Formula ...
Ali Al Khabyah +4 more
doaj +1 more source
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
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The line completion number of hypercubes
AKCE International Journal of Graphs and Combinatorics, 2019 In 1992, Bagga, Beineke, and Varma introduced the concept of the super line graph of index r of a graph G, denoted by ℒr(G). The vertices of ℒr(G)are the r-subsets of E(G), and two vertices S and T are adjacent if there exist s∈S and t∈T such that s and ...
S.A. Tapadia, B.N. Waphare
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Scattering theory and discrete-time quantum walks
, 2004 We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each.
Ambainis +21 more
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Multi-Line Geometry of Qubit-Qutrit and Higher-Order Pauli Operators [PDF]
, 2007 The commutation relations of the generalized Pauli operators of a qubit-qutrit system are discussed in the newly established graph-theoretic and finite-geometrical settings.
A. Blunck +14 more
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Bar 1-Visibility Drawings of 1-Planar Graphs
, 2013 A bar 1-visibility drawing of a graph $G$ is a drawing of $G$ where each vertex is drawn as a horizontal line segment called a bar, each edge is drawn as a vertical line segment where the vertical line segment representing an edge must connect the ...
A.M. Dean +13 more
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