Structural Properties and Hamiltonicity of Neighborhood Graphs |
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| Authors: | Ingo Schiermeyer Martin Sonntag Hanns-Martin Teichert |
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| Institution: | 1. Faculty of Mathematics and Computer Science, Freiberg University of Mining and Technology, Prüferstr. 1, 09596, Freiberg, Germany
2. Institute of Mathematics, University of Lübeck, Wallstr. 40, 23560, Lübeck, Germany
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| Abstract: | Let G = (V, E) be a simple undirected graph. N(G) = (V, E N ) is the neighborhood graph of the graph G, if and only if $$E_N = \{\{a,b\}\,|\, a \neq b\,\wedge\,\exists\, x \, \in V: \{x,a\} \in E \, \wedge \, \{x,b\} \in E \}.$$ We present several structural properties of N(G) and characterize the hamiltonicity of N(G) by means of chords of a hamiltonian cycle in G. |
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