Neighborhoods in line graphs
Ľubomír Šoltés (1990)
Acta Universitatis Carolinae. Mathematica et Physica
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Ľubomír Šoltés (1990)
Acta Universitatis Carolinae. Mathematica et Physica
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Gurusamy Rengasamy Vijayakumar (2013)
Discussiones Mathematicae Graph Theory
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The infimum of the least eigenvalues of all finite induced subgraphs of an infinite graph is defined to be its least eigenvalue. In [P.J. Cameron, J.M. Goethals, J.J. Seidel and E.E. Shult, Line graphs, root systems, and elliptic geometry, J. Algebra 43 (1976) 305-327], the class of all finite graphs whose least eigenvalues ≥ −2 has been classified: (1) If a (finite) graph is connected and its least eigenvalue is at least −2, then either it is a generalized line graph or it is represented...
A. K. Dewdney, Frank Harary (1976)
Czechoslovak Mathematical Journal
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Halina Bielak (1983)
Časopis pro pěstování matematiky
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Petrović, Miroslav, Milekić, Bojana (2000)
Publications de l'Institut Mathématique. Nouvelle Série
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Gliviak, Ferdinand, Kyš, P. (1997)
Acta Mathematica Universitatis Comenianae. New Series
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Petrović, Miroslav (1991)
Publications de l'Institut Mathématique. Nouvelle Série
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Daniel C. Slilaty, Thomas Zaslavsky (2015)
Discussiones Mathematicae Graph Theory
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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., edge-signed graphs whose line graphs, with the naturally induced vertex signature, are consistent. Their proof applies Hoede’s relatively difficult characterization of consistent vertex-signed graphs. We give a simple proof that does...