Covering energy of posets and its bounds

Vandana P. Bhamre; Madhukar M. Pawar

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 4, page 537-553
  • ISSN: 0862-7959

Abstract

top
The concept of covering energy of a poset is known and its McClelland type bounds are available in the literature. In this paper, we establish formulas for the covering energy of a crown with 2 n elements and a fence with n elements. A lower bound for the largest eigenvalue of a poset is established. Using this lower bound, we improve the McClelland type bounds for the covering energy for some special classes of posets.

How to cite

top

Bhamre, Vandana P., and Pawar, Madhukar M.. "Covering energy of posets and its bounds." Mathematica Bohemica 148.4 (2023): 537-553. <http://eudml.org/doc/299461>.

@article{Bhamre2023,
abstract = {The concept of covering energy of a poset is known and its McClelland type bounds are available in the literature. In this paper, we establish formulas for the covering energy of a crown with $2n$ elements and a fence with $n$ elements. A lower bound for the largest eigenvalue of a poset is established. Using this lower bound, we improve the McClelland type bounds for the covering energy for some special classes of posets.},
author = {Bhamre, Vandana P., Pawar, Madhukar M.},
journal = {Mathematica Bohemica},
keywords = {covering energy of poset; eigenvalue; spectrum; upper bound; lower bound},
language = {eng},
number = {4},
pages = {537-553},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Covering energy of posets and its bounds},
url = {http://eudml.org/doc/299461},
volume = {148},
year = {2023},
}

TY - JOUR
AU - Bhamre, Vandana P.
AU - Pawar, Madhukar M.
TI - Covering energy of posets and its bounds
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 4
SP - 537
EP - 553
AB - The concept of covering energy of a poset is known and its McClelland type bounds are available in the literature. In this paper, we establish formulas for the covering energy of a crown with $2n$ elements and a fence with $n$ elements. A lower bound for the largest eigenvalue of a poset is established. Using this lower bound, we improve the McClelland type bounds for the covering energy for some special classes of posets.
LA - eng
KW - covering energy of poset; eigenvalue; spectrum; upper bound; lower bound
UR - http://eudml.org/doc/299461
ER -

References

top
  1. Adiga, C., Bayad, A., Gutman, I., Srinivas, S. A., The minimum covering energy of a graph, Kragujevac J. Sci. 34 (2012), 39-56. (2012) 
  2. ndağ, Ş. B. Altı, Bozkurt, D., Lower bounds for the energy of (bipartite) graphs, MATCH Commun. Math. Comput. Chem. 77 (2017), 9-14. (2017) Zbl1466.92242MR3645362
  3. Collatz, L., Sinogowitz, U., 10.1007/BF02941924, Abh. Math. Semin. Univ. Hamb. 21 (1957), 63-77 German. (1957) Zbl0077.36704MR0087952DOI10.1007/BF02941924
  4. Cvetković, D. M., Doob, M., Sachs, H., Spectra of Graphs: Theory and Application, Academic Press, New York (1980). (1980) Zbl0458.05042MR0572262
  5. Das, K. C., Mojallal, S. A., Gutman, I., Improving McClelland's lower bounds for energy, MATCH Commun. Math. Comput. Chem. 70 (2013), 663-668. (2013) Zbl1299.05213MR3155011
  6. Davey, B. A., Priestley, H. A., 10.1017/CBO9780511809088, Cambridge University Press, Cambridge (1990). (1990) Zbl1002.06001MR1058437DOI10.1017/CBO9780511809088
  7. Grätzer, G., 10.1007/978-3-0348-7633-9, Pure and Applied Mathematics 75. Academic Press, New York (1978). (1978) Zbl0436.06001MR0509213DOI10.1007/978-3-0348-7633-9
  8. Gutman, I., The energy of a graph, Ber. Math.-Stat. Sekt. Forschungszent. Graz 103 (1978), 22 pages. (1978) Zbl0402.05040MR0525890
  9. Gutman, I., Furtula, B., 10.5562/cca3189, Croat. Chem. Acta 90 (2017), 359-368. (2017) DOI10.5562/cca3189
  10. Gutman, I., Furtula, B., Energies of Graphs: Survey, Census, Bibliography, Center for Scientific Research, Kragujevac (2019). (2019) 
  11. Gutman, I., Ramane, H. S., Research on graph energies in 2019, MATCH Commun. Math. Comput. Chem. 84 (2020), 277-292. (2020) 
  12. Hückel, E., 10.1007/BF01339530, Z. Phys. 70 (1931), 204-286 German. (1931) Zbl0002.09601DOI10.1007/BF01339530
  13. Indulal, G., Vijayakumar, A., A note on energy of some graphs, MATCH Commun. Math. Comput. Chem. 59 (2008), 269-274. (2008) Zbl1164.05040MR2381442
  14. Kelly, D., Rival, I., 10.4153/CJM-1974-120-2, Can. J. Math. 27 (1974), 1257-1271. (1974) Zbl0271.06003MR0417003DOI10.4153/CJM-1974-120-2
  15. Li, X., Shi, Y., Gutman, I., 10.1007/978-1-4614-4220-2, Springer, Berlin (2012). (2012) Zbl1262.05100MR2953171DOI10.1007/978-1-4614-4220-2
  16. McClelland, B. J., 10.1063/1.1674889, J. Chem. Phys. 54 (1971), 640-643. (1971) DOI10.1063/1.1674889
  17. Pawar, M. M., Bhamare, V. P., On covering energy of posets, Math. Sci. Int. Research J. 4 (2015), 121-125. (2015) 
  18. Pawar, M. M., Bhamre, V. P., 10.18311/jims/2020/25451, J. Indian Math. Soc., New Ser. 87 (2020), 193-205. (2020) Zbl1463.06005MR4123472DOI10.18311/jims/2020/25451
  19. Pawar, M. M., Bhangale, S. T., 10.1142/S1793557121501278, Asian-Eur. J. Math. 14 (2021), Article 2150127, 14 pages. (2021) Zbl1473.05184MR4292510DOI10.1142/S1793557121501278
  20. Rival, I., 10.4153/CMB-1974-016-3, Can. Math. Bull. 17 (1974), 91-95. (1974) Zbl0293.06003MR0360387DOI10.4153/CMB-1974-016-3
  21. Thakare, N. K., Pawar, M. M., Waphare, B. N., 10.1023/A:1022314517291, Period. Math. Hung. 45 (2002), 147-160. (2002) Zbl1026.06003MR1955202DOI10.1023/A:1022314517291

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.