Geodesic
Tetracyclic harmonic graphs
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 27 (2002) no. 1.

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

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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     title = {Tetracyclic harmonic graphs},
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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/