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Bulletin: Classe des sciences mathématiques et natturalles - Sciences mathématiques
2002, vol. 123, br. 27, str. 19-31
jezik rada: engleski
neklasifikovan
doi:10.2298/BMAT0227019B
Tetracyclic harmonic graphs
(naslov ne postoji na srpskom)
Borovićanin Bojana D., Gutman Ivan, Petrović M.
Univerzitet u Kragujevcu, Prirodno-matematički fakultet

Sažetak

(ne postoji na srpskom)
A graph G on n vertices v1, v2,..., vn is said to be harmonic if (d(v1),d(v2),..., d(vn))t is an eigenvector of its (0,1)-adjacency matrix where d(vi) is the degree ‚(= number of first neighbors) of the vertex Vi i = 1,2,..., 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.

Ključne reči

harmonic graphs; spectra (of graphs); walks

Reference

CrossRefMathSciNetKoBSON2

Borovićanin, B., Grunewald, S., Gutman, I., Petrović, M. (2003) Harmonic graphs with small number of cycles

226

Cvetković, D.M., Doob, M., Sachs, H. (1995) Spectra of graphs: Theory and application. Heidelberg-Leipzig: Barth Verlag

CrossRefMathSciNetKoBSON14

Cvetković, D.M., Petrić, M. (1984) A table of connected graphs on six vertices. Discrete Mathematics, 50, 1, 37-49

CrossRefMathSciNetKoBSON2

Dress, A., Gutman, I. (2003) The number of walks in a graph

CrossRefMathSciNetKoBSON1

Dress, A., Gutman, I. (2003) Asymptotic results regarding the number of walks in a graph

KoBSON2

Grunewald, S. (2003) Harmonic trees. Applied Mathematics Letters, 15, 1001-1004

CrossRefPubMedChemPortKoBSON5

Gutman, I. (2001) On walks in molecular graphs