## Članak

 članak: 1 od 1
Bulletin: Classe des sciences mathématiques et natturalles - Sciences mathématiques
2005, vol. 131, br. 30, str. 93-99
članak
doi:10.2298/BMAT0530093P

On the spectral radius of bicyclic graphs
(naslov ne postoji na srpskom)
aUniverzitet u Kragujevcu, Prirodno-matematički fakultet
bYancheng Teachers College - Department of Mathematics, Yancheng, Jiangsu, P. R. China

### Sažetak

(ne postoji na srpskom)
Let K3 and K'3 be two complete graphs of order 3 with disjoint vertex sets Let  be the 5-vertex graph, obtained by identifying a vertex of K3 with a vertex of K'3. Let  be the 4-vertex graph, obtained by identifying two vertices of K3 each with a vertex of K'3. Let  be graph of order n, obtained by attaching k paths of almost equal length to the vertex of degree 4 of . Let  be the graph of order n obtained by attaching k paths of almost equal length to a vertex of degree 3 of . Let  be the set of all connected bicyclic graphs of order n, possessing k pendent vertices. One of the authors recently proved that among the elements of , either  or  have the greatest spectral radius. We now show that for k ≥ 1 and n ≥ k + 5, among the elements of , the graph  has the greatest spectral radius.

### Reference

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Cvetković, D.M., Rowlinson, P. (1988) On connected graphs with maximal index. Publications de l'Institut mathematique, 44, 29-34
Cvetković, D.M., Rowlinson, P. (1990) The largest eigenvalue of a graph: A survey. Linear and Multilinear Algebra, 28(1): 3
Guo, S.G. (2005) The spectral radius of unicyclic and bicyclic graphs with n vertices and k pendant vertices. Linear Algebra and its Applications, 408, 78-85