The change of Seidel energy of tripartite Turán graph due to edge deletion

Abstract

Let S(G) be the Seidel matrix of a graph G. The Seidel energy of G, denoted by E_S(G), is defined to be the sum of absolute values of all eigenvalues of the Seidel matrix S(G) of G. In this paper, we consider the change of Seidel energy of graphs due to edge deletion. It is proved that the Seidel energy of the tripartite Turán graph T(n, 3) of order n ≥ 9 is always increased when an edge is deleted.

Keywords:

• Seidel energy
• Seidel energy change
• edge deletion
• Turán graph
• quotient matrix

AMS classifications:

• 05C50
• 15A18

Acknowledgments

The authors would like to thank the anonymous referees for careful reading of our manuscript and for invaluable comments. This work was supported by the National Natural Science Foundation of China (No. 11801521).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors would like to thank the anonymous referees for careful reading of our manuscript and for invaluable comments. This work was supported by the National Natural Science Foundation of China [grant number 11801521].