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Characterization of Trivalent Graphs with Minimal Eigenvalue Gap

Clemens Brand
Barry Guiduli
Wilfried Imrich

Puni tekst: engleski, pdf (276 KB) str. 193-201 preuzimanja: 534* citiraj
APA 6th Edition
Brand, C., Guiduli, B. i Imrich, W. (2007). Characterization of Trivalent Graphs with Minimal Eigenvalue Gap. Croatica Chemica Acta, 80 (2), 193-201. Preuzeto s https://hrcak.srce.hr/12850
MLA 8th Edition
Brand, Clemens, et al. "Characterization of Trivalent Graphs with Minimal Eigenvalue Gap." Croatica Chemica Acta, vol. 80, br. 2, 2007, str. 193-201. https://hrcak.srce.hr/12850. Citirano 12.12.2019.
Chicago 17th Edition
Brand, Clemens, Barry Guiduli i Wilfried Imrich. "Characterization of Trivalent Graphs with Minimal Eigenvalue Gap." Croatica Chemica Acta 80, br. 2 (2007): 193-201. https://hrcak.srce.hr/12850
Harvard
Brand, C., Guiduli, B., i Imrich, W. (2007). 'Characterization of Trivalent Graphs with Minimal Eigenvalue Gap', Croatica Chemica Acta, 80(2), str. 193-201. Preuzeto s: https://hrcak.srce.hr/12850 (Datum pristupa: 12.12.2019.)
Vancouver
Brand C, Guiduli B, Imrich W. Characterization of Trivalent Graphs with Minimal Eigenvalue Gap. Croatica Chemica Acta [Internet]. 2007 [pristupljeno 12.12.2019.];80(2):193-201. Dostupno na: https://hrcak.srce.hr/12850
IEEE
C. Brand, B. Guiduli i W. Imrich, "Characterization of Trivalent Graphs with Minimal Eigenvalue Gap", Croatica Chemica Acta, vol.80, br. 2, str. 193-201, 2007. [Online]. Dostupno na: https://hrcak.srce.hr/12850. [Citirano: 12.12.2019.]

Sažetak
Among all trivalent graphs on n vertices, let Gn be one with the smallest possible eigenvalue gap. (The eigenvalue gap is the difference between the two largest eigenvalues of the adjacency
matrix; for regular graphs, it equals the second smallest eigenvalue of the Laplacian matrix.) We show that Gn is unique for each n and has maximum diameter. This extends work of Guiduli and solves a conjecture implicit in a paper of Bussemaker, Čobeljić, Cvetković and Seidel. Depending on n, the graph Gn may not be the only one with maximum diameter. We thus also determine all cubic graphs with maximum diameter for a given number n of vertices.

Ključne riječi
trivalent graphs; eigenvalue gap; Laplacian matrix

Hrčak ID: 12850

URI
https://hrcak.srce.hr/12850

Posjeta: 806 *