Spectral distances in some sets of graphs
DOI:
https://doi.org/10.33044/revuma.1755Abstract
Some of the spectral distance related parameters (cospectrality, spectral eccentricity, and spectral diameter with respect to an arbitrary graph matrix) are determined in one particular set of graphs. According to these results, the spectral distances connected with the adjacency matrix and the corresponding distance related parameters are computed in some sets of trees. Examples are provided of graphs whose spectral distances related to the adjacency matrix, the Laplacian and the signless Laplacian matrix are mutually equal. The conjecture related to the spectral diameter of the set of connected regular graphs with respect to the adjacency matrix is disproved using graph energy.
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References
A. Abdollahi and M. R. Oboudi, Cospectrality of graphs, Linear Algebra Appl. 451 (2014), 169–181. MR 3198911.
A. Abdollahi, S. Janbaz and M. R. Oboudi, Distance between spectra of graphs, Linear Algebra Appl. 466 (2015), 401–408. MR 3278259.
S. M. Cioabă, W. H. Haemers, J. R. Vermette and W. Wong, The graphs with all but two eigenvalues equal to $pm1$, J. Algebraic Combin. 41 (2015), no. 3, 887–897. MR 3328184.
D. M. Cvetković, M. Doob and H. Sachs, Spectra of Graphs, third edition, Johann Ambrosius Barth, Heidelberg, 1995. MR 1324340.
D. Cvetković, P. Rowlinson and S. Simić, An Introduction to the Theory of Graph Spectra, London Mathematical Society Student Texts, 75, Cambridge University Press, Cambridge, 2010. MR 2571608.
F. Esser and F. Harary, On the spectrum of a complete multipartite graph, European J. Combin. 1 (1980), no. 3, 211–218. MR 0593991.
C. Godsil and G. Royle, Algebraic Graph Theory, Graduate Texts in Mathematics, 207, Springer-Verlag, New York, 2001. MR 1829620.
I. M. Jovanović, Some results on spectral distances of graphs, Rev. Un. Mat. Argentina 56 (2015), no. 2, 95–117. MR 3431817.
I. Jovanović and Z. Stanić, Spectral distances of graphs, Linear Algebra Appl. 436 (2012), no. 5, 1425–1435. MR 2890928.
I. Jovanović and Z. Stanić, Spectral distances of graphs based on their different matrix representations, Filomat 28 (2014), no. 4, 723–734. MR 3360065.
J. H. Koolen and V. Moulton, Maximal energy graphs, Adv. in Appl. Math. 26 (2001), no. 1, 47–52. MR 1806691.
Q. Li and K. Q. Feng, On the largest eigenvalue of a graph, Acta Math. Appl. Sinica 2 (1979), no. 2, 167–175. MR 0549045.
R. Liu, H. Jia and J. Shu, An edge-rotating theorem on the least eigenvalue of graphs, Acta Math. Appl. Sin. Engl. Ser. 31 (2015), no. 4, 945–952. MR 3418272.
D. Stevanović, Research problems from the Aveiro Workshop on Graph Spectra, Linear Algebra Appl. 423 (2007), no. 1, 172–181. MR 2312333.
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