Results 231 to 240 of about 390,128 (262)
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Journal of Graph Theory, 1981
AbstractSufficient conditions on the degrees of a graph are given in order that its line graph have a hamiltonian cycle.
Richard A. Brualdi, Robert F. Shanny
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AbstractSufficient conditions on the degrees of a graph are given in order that its line graph have a hamiltonian cycle.
Richard A. Brualdi, Robert F. Shanny
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Journal of Graph Theory, 1981
AbstractGeneralized line graphs extend the ideas of both line graphs and cocktail party graphs. They were originally motivated by spectral considerations. in this paper several (nonspectral) classical theorems about line graphs are extended to generalized line graphs, including the derivation and construction of the 31 minimal nongeneralized line ...
Dragos M. Cvetkovic +2 more
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AbstractGeneralized line graphs extend the ideas of both line graphs and cocktail party graphs. They were originally motivated by spectral considerations. in this paper several (nonspectral) classical theorems about line graphs are extended to generalized line graphs, including the derivation and construction of the 31 minimal nongeneralized line ...
Dragos M. Cvetkovic +2 more
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Ars Comb., 2012
Summary: The line graph of \(G\), denoted \(L(G)\), is the graph with vertex set \(E(G)\), where vertices \(x\) and \(y\) are adjacent in \(L(G)\) iff edges \(x\) and \(y\) share a common vertex in \(G\). In this paper we determine all graphs \(G\) for which \(L(G)\) is a circulant graph.
Jason I. Brown, Richard Hoshino
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Summary: The line graph of \(G\), denoted \(L(G)\), is the graph with vertex set \(E(G)\), where vertices \(x\) and \(y\) are adjacent in \(L(G)\) iff edges \(x\) and \(y\) share a common vertex in \(G\). In this paper we determine all graphs \(G\) for which \(L(G)\) is a circulant graph.
Jason I. Brown, Richard Hoshino
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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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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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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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Journal of Graph Theory, 1998
A simple graph \(\Gamma\) is said to be subpancyclic if it contains an (elementary) circuit of length \(k\) for every integer \(k\in[3,\text{cr}(\Gamma)]\), where \(\text{cr}(\Gamma)\) denotes the length of a longest circuit in \(\Gamma\). If \(\text{cr}(\Gamma)=|V(\Gamma)|\), then \(\Gamma\) is said to be pancyclic.
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A simple graph \(\Gamma\) is said to be subpancyclic if it contains an (elementary) circuit of length \(k\) for every integer \(k\in[3,\text{cr}(\Gamma)]\), where \(\text{cr}(\Gamma)\) denotes the length of a longest circuit in \(\Gamma\). If \(\text{cr}(\Gamma)=|V(\Gamma)|\), then \(\Gamma\) is said to be pancyclic.
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Sharp bounds on the Arithmetic–geometric index of graphs and line graphs
Discrete Applied Mathematics, 2022Minjie Zhang
exaly