The spectrum of infinite regular line graphs

Transactions of the American Mathematical Society

Volumn 352, Issue 1, 2000, Pages 115-132

  Shirai, Tomoyuki ^a,b  

^a UNIVERSITY OF TOKYO   (Japan)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Discrete laplacian; Para line graph; Regular line graph; Spectrum; Subdivision

Indexed keywords

EID: 22844454199     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-99-02497-6     Document Type: Article

References (7)

1. D. M. Cvctkovic, M. Doob and H. Sachs. Spectra of graphs-theory and application, Deutscher Verlag der Wissenschaften, Berlin, and Academic Press, New York, 1980.MR 81i: 05054
2. J. Dodziuk and L. Karp. Spectral and function theory for combinatorial Laplacians, A. M. S. Contemporary Mathematics 73 (1988), 25-40.MR 89h: 58220
3. Yu. Higuchi. Isoperimetric inequality and random walks on an infinite graph and its line graph, preprint.
4. Yu. Higuchi. Random Walks and Isoperimetric Inequalities on Infinite Planar Graphs and Their Duals, Dissertation, Univ. of Tokyo, January 1995.
5. B. Mohär and W. Woess. A survey of spectra of infinite graphs, Bull. London Math. Soc. 21 (1989), 209-234.MR 90d: 05162
6. M. Reed and B. Simon. Methods of Modern Mathematical Physics, vol. I, Academic Press, New York, 1980.MR 85e: 46002
7. T. Shima. On eigenvalue problems for the random uialks on the Sierpinski pre-gasket, Japan J. Indust. ADD!. Math.. 8 Ü9911. 127-141.MR 92c: 60094