On borderenergetic and L-borderenergetic graphs

Document Type: Original Article

Author

Department of Mathematics, Shahid Rajaee Teacher Training University

Abstract

A graph G of order n is said to be borderenergetic if its energy is equal to 2n − 2. In this paper, we study the borderenergetic and Laplacian borderenergetic graphs.

Graphical Abstract

On borderenergetic and L-borderenergetic graphs

Keywords


[1] B. Deng, X. Li, J. Wang, Further results on L-borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 77 (3) (2017) 607–616.

[2] B. Deng, X. Li, More on L-borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 77 (1) (2017) 115–127.

[3] B. Deng, X. Li, I. Gutman, More on borderenergetic graphs, Linear Algebra Appl. 497 (2016) 199– 208.

[4] B. Furtula, I. Gutman, Borderenergetic Graphs of Order 12, Iranian J. Math. Chem. 8 (4) (2017) 339–343.

[5] S. Gong, X. Li, G. Xu, I. Gutman, B. Furtula, Borderenergetic graphs, MATCH Commun. Math. Comput. Chem.74 (2015) 321–332.

[6] I. Gutman, The energy of a graph, Ber. Math-Statist. Sekt. Forschungszentrum Graz 103 (1978) 1–22.

[7] I. Gutman, The energy of a graph: old and new results, in: A. Betten, A. Kohner, R. Laue, A. Wassermann (Eds.), Algebraic Combinatorics and Applications, Springer, Berlin, (2001), 196–211.

[8] I. Gutman, B. Zhou, Laplacian energy of a graph, Linear Algebra Appl. 414 (2006) 29–37.

[9] I. Gutman, On Borderenergetic graphs, Bull. Acad. Serbe Sci. Arts (Cl. Math. Natur.) 42 (2017) 9–18.

[10] M. Hakimi-Nezhaad, M. Ghorbani, Laplacian Borderenergetic graphs, Journal of Information and Optimization Sciences, inpress.

[11] Y. Hou, I. Gutman, Hyperenergetic line graphs, MATCH Commun. Math. Comput. Chem. 43 (2001) 29–39.

[12] Y. Hou, Q. Tao, Borderenergetic threshold graphs, MATCH Commun. Math. Comput. Chem. 75 (2016) 253–262.

[13] X. Li, Y. Shi, I. Gutman, Graph energy, Springer, New York, 2012.

[14] X. Li, M. Wei, S. Gong, A computer search for the borderenergetic graphs of order 10, MATCH Commun. Math. Comput. Chem. 74 (2015) 333–342.

[15] X. Li, M. Wei, X. Zhu, Borderenergetic graphs with small maximum or large minimum degrees, MATCH Commun. Math. Comput. Chem. 77 (2016) 25–36.

[16] L. Lu, Q. Huang, On the existence of non-complete L−borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 77 (3) (2017) 625–634.

[17] Z. Shao, F. Deng, Correcting the number of borderenergetic graphs of order 10, MATCH Commun. Math. Comput. Chem. 75 (2016) 263–265.

[18] Q. Tao, Y. Hou, A computer search for the L-borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 77 (3) (2017) 595–606.

[19] F. Tura, L-borderenergetic graphs, MATCH Commun. Math. Comput. Chem. 77 (2017) 37–44. [20] F. Tura, L-borderenergetic graphs and normalized Laplacian energy. MATCH Commun. Math. Comput. Chem. 77 (3) (2017) 617–624.