Geodesic
Derived Graphs of Subdivision Graph
Kragujevac Journal of Mathematics, Tome 37 (2013) no. 2, p. 319 .

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 $[G]^\dagger$ of a graph $G$ is the graph having the same vertex set as $G$, two vertices of $[G]^\dagger$ being adjacent if and only if their distance in $G$ is two. In this paper the derived graphs of the subdivision graphs, their spectra and energies are determined.
Classification : 05C12 05C50 05C75
Keywords: Derived graph, Subdivision graph, Spectrum (of graph), Energy (of graph) 
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     author = {S. P. Hande and S. R. Jog and H. S. Ramane and P. R. Hampiholi and I. Gutman and B. S. Durgi},
     title = {Derived {Graphs} of {Subdivision} {Graph}},
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S. P. Hande; S. R. Jog; H. S. Ramane; P. R. Hampiholi; I. Gutman; B. S. Durgi. Derived Graphs of Subdivision Graph. Kragujevac Journal of Mathematics, Tome 37 (2013) no. 2, p. 319 . http://geodesic.mathdoc.fr/item/KJM_2013_37_2_a10/