Signed graphs with at most three eigenvalues

Farzaneh Ramezani; Peter Rowlinson; Zoran Stanić

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 1, page 59-77
  • ISSN: 0011-4642

Abstract

top
We investigate signed graphs with just 2 or 3 distinct eigenvalues, mostly in the context of vertex-deleted subgraphs, the join of two signed graphs or association schemes.

How to cite

top

Ramezani, Farzaneh, Rowlinson, Peter, and Stanić, Zoran. "Signed graphs with at most three eigenvalues." Czechoslovak Mathematical Journal 72.1 (2022): 59-77. <http://eudml.org/doc/298124>.

@article{Ramezani2022,
abstract = {We investigate signed graphs with just 2 or 3 distinct eigenvalues, mostly in the context of vertex-deleted subgraphs, the join of two signed graphs or association schemes.},
author = {Ramezani, Farzaneh, Rowlinson, Peter, Stanić, Zoran},
journal = {Czechoslovak Mathematical Journal},
keywords = {signed graph; join; adjacency matrix; main eigenvalue; net-degree; association scheme},
language = {eng},
number = {1},
pages = {59-77},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Signed graphs with at most three eigenvalues},
url = {http://eudml.org/doc/298124},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Ramezani, Farzaneh
AU - Rowlinson, Peter
AU - Stanić, Zoran
TI - Signed graphs with at most three eigenvalues
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 1
SP - 59
EP - 77
AB - We investigate signed graphs with just 2 or 3 distinct eigenvalues, mostly in the context of vertex-deleted subgraphs, the join of two signed graphs or association schemes.
LA - eng
KW - signed graph; join; adjacency matrix; main eigenvalue; net-degree; association scheme
UR - http://eudml.org/doc/298124
ER -

References

top
  1. elić, M. Anđ, Koledin, T., Stanić, Z., 10.7151/dmgt.2279, Discuss. Math., Graph Theory 40 (2020), 405-416. (2020) Zbl1433.05139MR4060992DOI10.7151/dmgt.2279
  2. Belardo, F., Cioabă, S. M., Koolen, J., Wang, J., 10.26493/2590-9770.1286.d7b, Art Discrete Appl. Math. 1 (2018), Article ID P2.10, 23 pages. (2018) Zbl1421.05052MR3997096DOI10.26493/2590-9770.1286.d7b
  3. Belardo, F., Simić, S. K., 10.1016/j.laa.2015.02.007, Linear Algebra Appl. 475 (2015), 94-113. (2015) Zbl1312.05078MR3325220DOI10.1016/j.laa.2015.02.007
  4. Chan, H. C., Rodger, C. A., Seberry, J., On inequivalent weighing matrices, Ars Comb. 21A (1986), 299-333. (1986) Zbl0599.05013MR0835757
  5. Cheng, X.-M., Gavrilyuk, A. L., Greaves, G. R. W., Koolen, J. H., 10.1016/j.ejc.2016.03.004, Eur. J. Comb. 56 (2016), 57-80. (2016) Zbl1335.05107MR3490095DOI10.1016/j.ejc.2016.03.004
  6. Cheng, X.-M., Greaves, G. R. W., Koolen, J. H., 10.1016/j.jctb.2017.09.004, J. Comb. Theory, Ser. B 129 (2018), 55-78. (2018) Zbl1379.05072MR3758241DOI10.1016/j.jctb.2017.09.004
  7. Colbourn, C. J., (eds.), J. H. Dinitz, 10.1201/9781420010541, Discrete Mathematics and its Applications. Chapman & Hall/CRC, Boca Raton (2007). (2007) Zbl1101.05001MR2246267DOI10.1201/9781420010541
  8. Cvetković, D., Doob, M., Sachs, H., Spectra of Graphs: Theory and Applications, J. A. Barth, Leipzig (1995). (1995) Zbl0824.05046MR1324340
  9. Cvetković, D., Rowlinson, P., Simić, S., 10.1017/CBO9780511801518, London Mathematical Society Student Texts 75. Cambridge University Press, Cambridge (2010). (2010) Zbl1211.05002MR2571608DOI10.1017/CBO9780511801518
  10. Harada, M., Munemasa, A., 10.1002/jcd.20295, J. Comb. Des. 20 (2012), 45-57. (2012) Zbl1252.05026MR2864617DOI10.1002/jcd.20295
  11. Hou, Y., Tang, Z., Wang, D., 10.1016/j.disc.2019.111615, Discrete Math. 342 (2019), Article ID 111615, 8 pages. (2019) Zbl1422.05049MR3990025DOI10.1016/j.disc.2019.111615
  12. McKee, J., Smyth, C., 10.1016/j.jalgebra.2007.05.019, J. Algebra 317 (2007), 260-290. (2007) Zbl1140.15007MR2360149DOI10.1016/j.jalgebra.2007.05.019
  13. Ramezani, F., On the signed graphs with two distinct eigenvalues, Util. Math. 114 (2020), 33-48. (2020) Zbl07274222MR4230326
  14. Ramezani, F., 10.1080/03081087.2020.1736979, (to appear) in Linear Multilinear Algebra. MR4388842DOI10.1080/03081087.2020.1736979
  15. Ramezani, F., Rowlinson, P., Stanić, Z., 10.1016/j.disc.2020.111982, Discrete Math. 343 (2020), Article ID 111982, 8 pages. (2020) Zbl07233221MR4107756DOI10.1016/j.disc.2020.111982
  16. Rowlinson, P., 10.1017/S0308210500014293, Proc. R. Soc. Edinb., Sect. A 99 (1985), 277-281. (1985) Zbl0562.05044MR0785534DOI10.1017/S0308210500014293
  17. Rowlinson, P., 10.1016/j.laa.2016.06.031, Linear Algebra Appl. 507 (2016), 462-473. (2016) Zbl1343.05096MR3536969DOI10.1016/j.laa.2016.06.031
  18. Rowlinson, P., 10.2298/AADM161111033R, Appl. Anal. Discrete Math. 11 (2017), 74-80. (2017) MR3648655DOI10.2298/AADM161111033R
  19. Seidel, J. J., Graphs and two-graphs, Proceedings of the 5th Southeastern Conference on Combinatorics, Graph Theory, and Computing Utilitas Mathematica Publication, Winnipeg (1974), 125-143. (1974) Zbl0308.05120MR0364028
  20. Simić, S. K., Stanić, Z., 10.1016/j.laa.2016.03.036, Linear Algebra Appl. 501 (2016), 390-408. (2016) Zbl1334.05056MR3485074DOI10.1016/j.laa.2016.03.036
  21. Stanić, Z., 10.1515/9783110351347, De Gruyter Series in Discrete Mathematics and Applications 4. De Gruyter, Berlin (2017). (2017) Zbl1370.05002MR3753662DOI10.1515/9783110351347
  22. Stanić, Z., 10.26493/1855-3974.1740.803, Ars Math. Contemp. 17 (2019), 103-114. (2019) Zbl1433.05142MR3998150DOI10.26493/1855-3974.1740.803
  23. Stanić, Z., 10.1016/j.dam.2019.06.017, Discrete Appl. Math. 271 (2019), 184-190 corrigendum ibid. 284 640 2020. (2019) Zbl1428.05331MR4030312DOI10.1016/j.dam.2019.06.017
  24. Stanić, Z., 10.1016/j.amc.2019.124627, Appl. Math. Comput. 364 (2020), Article ID 124627, 9 pages. (2020) Zbl1433.05210MR3996372DOI10.1016/j.amc.2019.124627
  25. Dam, E. R. van, 10.1006/jctb.1998.1815, J. Comb. Theory, Ser. B 73 (1998), 101-118. (1998) Zbl0917.05044MR1631983DOI10.1006/jctb.1998.1815
  26. Dam, E. R. van, 10.1023/A:1018628204156, J. Algebr. Comb. 10 (1999), 69-107. (1999) Zbl0929.05096MR1701285DOI10.1023/A:1018628204156
  27. Zaslavsky, T., 10.1016/0166-218X(82)90033-6, Discrete Appl. Math. 4 (1982), 47-74. (1982) Zbl0476.05080MR0676405DOI10.1016/0166-218X(82)90033-6
  28. Zaslavsky, T., Matrices in the theory of signed simple graphs, Advances in Discrete Mathematics and Applications Ramanujan Mathematical Society Lecture Notes Series 13. Ramanujan Mathematical Society, Mysore (2010), 207-229. (2010) Zbl1231.05120MR2766941

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.