Results 301 to 310 of about 1,844,339 (310)
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Acta Mathematica Scientia, 1998
For a graph \(G\), let \(\overline {\sigma}_2\) denote min\(\{ d(u) + d(v)\mid uv \in E(G) \}\). The author shows that if \(G\) is connected and of order \(n \geq 43\) such that the line graph \(L(G)\) is Hamiltonian and \(\overline {\sigma}_2> 2(n/5 - 1)\), then \(L(G)\) is pancyclic. This settles a conjecture of Benhocine et al. For a connected graph
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For a graph \(G\), let \(\overline {\sigma}_2\) denote min\(\{ d(u) + d(v)\mid uv \in E(G) \}\). The author shows that if \(G\) is connected and of order \(n \geq 43\) such that the line graph \(L(G)\) is Hamiltonian and \(\overline {\sigma}_2> 2(n/5 - 1)\), then \(L(G)\) is pancyclic. This settles a conjecture of Benhocine et al. For a connected graph
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On Eulerian and Hamiltonian Graphs and Line Graphs
Canadian Mathematical Bulletin, 1965A graph G has a finite set V of points and a set X of lines each of which joins two distinct points (called its end-points), and no two lines join the same pair of points. A graph with one point and no line is trivial. A line is incident with each of its end-points. Two points are adjacent if they are joined by a line.
C. St. J. A. Nash-Williams, Frank Harary
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Mathematical Programming, 1978
Line-perfect graphs have been defined by L.E. Trotter as graphs whose line-graphs are perfect. They are characterized by the property of having no elementary odd cycle of size larger than 3. L.E. Trotter showed constructively that the maximum cardinality of a set of mutually non-adjacent edges (matching) is equal to the minimum cardinality of a ...
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Line-perfect graphs have been defined by L.E. Trotter as graphs whose line-graphs are perfect. They are characterized by the property of having no elementary odd cycle of size larger than 3. L.E. Trotter showed constructively that the maximum cardinality of a set of mutually non-adjacent edges (matching) is equal to the minimum cardinality of a ...
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Graphs and Combinatorics, 1987
The line domination number of a graph is the minimum number of edges with the property that every other edge is adjacent to some of these edges. Several results, especially bounds, on this number are presented.
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The line domination number of a graph is the minimum number of edges with the property that every other edge is adjacent to some of these edges. Several results, especially bounds, on this number are presented.
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Journal of Graph Theory, 1984
AbstractWe give best possible Ore‐like conditions for a graph so that its line graph is Hamiltonian.
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AbstractWe give best possible Ore‐like conditions for a graph so that its line graph is Hamiltonian.
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Mathematical Programming, 1977
The concept of line perfection of a graph is defined so that a simple graph is line perfect if and only if its line graph is perfect in the usual sense. Line perfect graphs are characterized as those which contain no odd cycles of size larger than 3.
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The concept of line perfection of a graph is defined so that a simple graph is line perfect if and only if its line graph is perfect in the usual sense. Line perfect graphs are characterized as those which contain no odd cycles of size larger than 3.
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Properties of spectra of graphs and line graphs
Applied Mathematics-A Journal of Chinese Universities, 2002Using the interlacing theorem for eigenvalues of real symmetric matrices several straightforward inequalities for eigenvalues of the following graph matrices are derived: the Laplacian matrix and a related matrix of a graph, and the adjacency matrix of the line graph of a graph.
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2005
Publisher Summary This chapter covers the basics of customizing line graphs using keywords with the PLOT and OPLOT commands. The plotting symbol is specified with the PSYM keyword. Lines connecting the plot symbols are turned on by making PSYMnegative. The line style is specified with the LINESTYLE keyword.
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Publisher Summary This chapter covers the basics of customizing line graphs using keywords with the PLOT and OPLOT commands. The plotting symbol is specified with the PSYM keyword. Lines connecting the plot symbols are turned on by making PSYMnegative. The line style is specified with the LINESTYLE keyword.
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