Q-borderenergetic threshold graphs
DOI:
https://doi.org/10.5902/2179460X39755Keywords:
signless laplacian energy, threshold graphAbstract
A graph G is said to be borderenergetic (L-borderenergetic, respectively) if its energy (Laplacian energy, respectively) equals the energy (Laplacian energy, respectively) of the complete graph. Recently, this concept was extend to signless Laplacian energy (see Tao, Q., Hou, Y. (2018). Q-borderenergetic graphs. AKCE International Journal of Graphs and Combinatorics). A graph G is called Q-borderenergetic if its signless Laplacian energy is the same of the complete graph Kn; i.e., QE(G) = QE(Kn) = 2n - 2: In this paper, we investigate Q-borderenergetic graphs on the class of threshold graphs. For a family of threshold graphs of order n <= 100; we find out exactly 13 graphs such that QE(G) = 2n- 2:
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References
Fritscher, E., Trevisan, V. (2016). Exploring symmetries to decompose matrices and graphs preserving the spectrum. SIAM J
Matrix Anal Appl, 37, 260–289.
Gong, S., Li, X., Xu, G., Gutman, I., Furtula, B. (2015). Borderenergetic graphs. MATCH Commun Math Comput Chem, 74,
–332.
Hou, Y., Tao, Q. (2016). Borderenergetic threshold graphs. MATCH Commun Math Comput Chem, 75, 253–262.
Jacobs, D. P., Trevisan, V., Tura, F. (2015). Eigenvalues and energy in threshold graphs. Lin Algebra Appl, 465, 412–425.
Li, X., Shi, Y., Gutman, I. (2012). Graph Energy. Springer, New York.
Li, X., Wei, M., Gong, S. (2015). A computer search for the borderenergetic graphs of order 10. MATCH Commun Math Comput
Chem, 74, 333–342.
Mahadev, N. V. R., Peled, U. N. (1995). Threshold graphs and related topics. Elsevier.
Shao, Z., Deng, F. (2016). Correcting the number of borderenergetic graphs of order 10. MATCH Commun Math Comput Chem,
, 263–266.
Tao, Q., Hou, Y. (2018). Q-borderenergetic graphs. AKCE International Journal of Graphs and Combinatorics.
Tura, F. (2017). L-borderenergetic graphs. MATCH Commun Math Comput Chem, 77, 37–44.
Yu, L., Zhang, Y., Jian, G., Gutman, I. (2016). More on borderenergetic graphs. Lin Algebra Appl, 497, 199–208.
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