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Communications in Nonlinear Science and Numerical Simulation, 2017
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Wiktor Warchalowski +1 more
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Wiktor Warchalowski +1 more
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Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009
In this paper we investigate discrete linear search and graph search problems. It is well-known that the Bounded Discrete Linear Search Problem (BDLSP) can be solved efficiently using a dynamic programming approach. However, we show that its generalization to the graph case—the Graph Search Problem (GSP)—is NP-complete. We further consider the Discrete
Hua Li, Edwin K. P. Chong
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In this paper we investigate discrete linear search and graph search problems. It is well-known that the Bounded Discrete Linear Search Problem (BDLSP) can be solved efficiently using a dynamic programming approach. However, we show that its generalization to the graph case—the Graph Search Problem (GSP)—is NP-complete. We further consider the Discrete
Hua Li, Edwin K. P. Chong
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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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On the resistance diameters of graphs and their line graphs
Discrete Applied Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Si-Ao Xu +3 more
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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, 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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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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