Geodesic
Spectra of copies of Bethe trees attached to path and applications
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 33 (2008), p. 59 .

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The Bethe tree $B_{d,k}$ is the rooted tree of $k$ levels whose root vertex has degree $d$ , the vertices from level 2 to level $k-1$ have degree $d+1$ , and the vertices at level $k$ have degree 1. This paper gives a decomposition of the characteristic polynomial of the adacency matrix of the tree $T(d,k,r)$ , obtained by attaching copies of $B(d,k)$ to the vertices of the $r$-vertex path. Moreover, lower and upper bounds for the energy of $T(d,k,r)$ are obtained.
Classification : 05C50
Keywords: spectrum (of graph), energy (of graph), Bethe tree 
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     author = {Mar{\'\i}a Robbiano and I. Gutman and R. Jim\'enez and B. San Martin},
     title = {Spectra of copies of {Bethe} trees attached to path and applications},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {59 },
     publisher = {mathdoc},
     volume = {33},
     year = {2008},
     zbl = {1199.05240},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASS_2008_33_a3/}
}
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María Robbiano; I. Gutman; R. Jiménez; B. San Martin. Spectra of copies of Bethe trees attached to path and applications. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 33 (2008), p. 59 . http://geodesic.mathdoc.fr/item/BASS_2008_33_a3/