On the Laplacian Szeged Spectrum of Paths

Document Type : Research Paper

Author

Faculty of Civil Engineering, University of Zagreb

Abstract

We present explicit formulas for the Laplacian Szeged eigenvalues of paths, grids, $C_4$-nanotubes
and of Cartesian products of paths with some other simple graphs. A number of open problems is listed.

Keywords

References

  1. G‎. ‎E‎. ‎Andrews‎, ‎W‎. ‎Gawronski‎ and ‎L‎. ‎L‎. ‎Littlejohn‎, ‎The Legendre-Stirling numbers‎, ‎Discrete Math. 311 (2011) 1255–1272‎. ‎
  2. ‎N‎. ‎Biggs‎, ‎Algebraic Graph Theory‎, Cambridge Univ‎. ‎Press‎, ‎Cambridge‎, ‎1974‎. ‎
  3. M‎. ‎Bruschi‎, ‎F‎. ‎Calogero‎ and ‎R‎. ‎Droghei‎, Proof of certain Diophantine conjectures and identification of‎ ‎remarkable classes of orthogonal polynomials‎, ‎J‎. ‎Phys‎. ‎A‎: ‎Math‎. ‎Theor. 40 (2007) 3815–3829‎. ‎
  4. ‎D‎. ‎M‎. ‎Cvetković‎, ‎M‎. ‎Doob‎ and ‎H‎. ‎Sachs‎, ‎Spectra of Graphs‎, ‎Academic Press‎, ‎New York‎, ‎1980‎. ‎‎
  5. G‎. ‎H‎. ‎Fath-Tabar‎, ‎T‎. ‎Došlić ‎and A‎. ‎R‎. ‎Ashrafi‎, ‎On the Szeged and the Laplacian Szeged spectrum of a graph‎, ‎Linear Algebra ‎Appl. 433 (2010) 662–671‎. ‎
  6. C‎. ‎M‎. ‎da Fonseca and ‎E‎. ‎Kiliç‎, A new type of Sylvester–Kac matrix and its spectrum‎, Linear Multilinear Algebra‎, ‎to appear‎. ‎
  7. ‎C‎. ‎D‎. ‎Godsil‎, ‎Algebraic Combinatorics‎, Chapman and Hall‎, ‎New York‎, ‎1993‎. ‎
  8. ‎I‎. ‎Gutman‎, ‎A formula for the Wiener number of trees and its extension to the graphs containing cycles‎, ‎Graph Theory Notes of New York XVII (1994) 9–15‎. ‎
  9. ‎I‎. ‎Gutman‎, ‎A‎. ‎A‎. ‎Dobrynin‎, ‎The Szeged index-‎a success story‎, Graph Theory Notes New York 34 (1998) 37–44‎. ‎
  10. ‎J‎. ‎Schwinger, On Angular Momentum‎,‎ Unpublished Report‎, ‎Harvard University‎, ‎Nuclear Development Associates‎, ‎Inc.‎, ‎United States Department of Energy (through predecessor agency the Atomic Energy Commission)‎, ‎Report Number NYO-3071 (January 26‎, ‎1952)‎. ‎
  11. ‎ ‎N‎. ‎J‎. ‎A‎. ‎Sloane‎, (ed.), ‎The On-Line Encyclopedia of Integer Sequences‎, ‎published electronically at http://oeis.org‎. ‎
  12. ‎D‎. ‎B‎. ‎West‎, Introduction to Graph Theory‎, Prentice Hall‎, ‎Upper Saddle River‎, ‎1996‎. ‎
  13. ‎H‎. ‎Wiener‎, ‎Structural determination of paraffin boiling points‎, J‎. ‎Am‎. ‎Chem‎. ‎Soc. 69 (1947) 17–20‎. ‎
Iranian Journal of Mathematical Chemistry
Volume 11, Issue 1
March 2020
Pages 57-63

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