Geodesic
Tetracyclic harmonic graphs
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 27 (2002) no. 1 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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A graph $G$ on $n$ vertices $v_1,v_2,\ldots,v_n$ is said to be harmonic if $(d(v_1),d(v_2),\ldots,d(v_n))^t$ is an eigenvector of its $(0,1)$-ađacency matrix, where $d(v_i)$ is the degree (= number of first neighbors) of the vertex $v_i \ , \ i=1,2,\ldots,n$ . Earlier all acyclic, unicyclic, bicyclic and tricyclic harmonic graphs were characterized. We now show that there are 2 regular and 18 non-regular connected tetracyclic harmonic graphs and determine their structures. 
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     author = {B. Borovi\'canin and I. Gutman and M. Petrovi\'c},
     title = {Tetracyclic harmonic graphs},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {19 - 31},
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B. Borovićanin; I. Gutman; M. Petrović. Tetracyclic harmonic graphs. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 27 (2002) no. 1. http://geodesic.mathdoc.fr/item/BASS_2002_27_1_a1/