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

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Tetracyclic harmonic graphs

B. Borovicanin, I. Gutman and M. Petrovic

Faculty of Science, University of Kragujevac, P. O. Box 60, YU–34000 Kragujevac, Yugoslavia

Abstract: 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 non-regular connected tetracyclic harmonic graphs and determine their structures.

Keywords: Harmonic graphs, Spectra (of graphs), Walks

Classification (MSC2000): 05C50, 05C75

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Electronic fulltext finalized on: 22 Sep 2002. This page was last modified: 20 Jun 2011.

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