Geodesic
Derived graphs of some graphs
Kragujevac Journal of Mathematics, Tome 36 (2012) no. 2, p. 309

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The derived graph of a simple graph $G$, denoted by $G^\dagger$, is the graph having the same vertex set as $G$, in which two vertices are adjacent if and only if their distance in $G$ is two. Continuing the studies communicated in Kragujevac J. Math. {\bf 34} (2010), 139-146, we examined derived graphs of some graphs and determine their spectra.
Classification : 05C12 05C50 05C75
Keywords: Derived graph, spectrum (of graph), second-stage spectrum (of graph) 
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Sudhir R. Jog; Satish P. Hande; Ivan Gutman; S. Burcu Bozkurt. Derived graphs of some graphs. Kragujevac Journal of Mathematics, Tome 36 (2012) no. 2, p. 309 . http://geodesic.mathdoc.fr/item/KJM_2012_36_2_a13/