Geodesic
Walk counts and the spectral radius of graphs
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 40 (2015) no. 1.

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

We develop a new method that uses walk counts for comparing spectral radii of graphs similar in a precisely defined fashion. The method is applied to the cases where a path-like or a star-like structure is coalesced to a graph, in order to prove weak inequality in the conjectured inequality of Belardo, Li Marzi and Simić, and to resolve the Brualdi-Solheid problem for the classes of graphs consisting of rooted products with the same rooted graph. 
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     author = {Dragan Stevanovi\'c},
     title = {Walk counts and the spectral radius of graphs},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {33 - 57},
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Dragan Stevanović. Walk counts and the spectral radius of graphs. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 40 (2015) no. 1. http://geodesic.mathdoc.fr/item/BASS_2015_40_1_a3/