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A characterization of graphs with supereulerian line graphs
International Journal of Computer Mathematics: Computer Systems Theory, 2020The line graph L(G) of a graph G is a simple graph with E(G) being its vertex set, where two vertices are adjacent in L(G) whenever the corresponding edges share a common vertex in G.
Yufei Huang 0007 +4 more
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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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Pattern Recognition Letters, 1993
The author defines and studies the concept of a fuzzy line graph of a fuzzy graph. The necessary and sufficient conditions for a fuzzy graph to be isomorphic to its corresponding fuzzy line graph are given. Also established is a necessary and sufficient condition for a fuzzy graph to be a fuzzy line graph of a fuzzy graph.
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The author defines and studies the concept of a fuzzy line graph of a fuzzy graph. The necessary and sufficient conditions for a fuzzy graph to be isomorphic to its corresponding fuzzy line graph are given. Also established is a necessary and sufficient condition for a fuzzy graph to be a fuzzy line graph of a fuzzy graph.
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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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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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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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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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