Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques Vol. CXXIII, No. 27, pp. 19–31 (2002) 

Tetracyclic harmonic graphsB. Borovicanin, I. Gutman and M. PetrovicFaculty of Science, University of Kragujevac, P. O. Box 60, YU–34000 Kragujevac, YugoslaviaAbstract: 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 $(0,1)$adjacency 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 nonregular connected tetracyclic harmonic graphs and determine their structures. Keywords: Harmonic graphs, Spectra (of graphs), Walks Classification (MSC2000): 05C50, 05C75 Full text of the article: (for faster download, first choose a mirror)
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