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}},
     journal = {Kragujevac Journal of Mathematics},
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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/