New bounds for Seidel energy of graphs

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, College of Science, Shiraz University, Shiraz, Iran

2 Sama Technical and Vocational School, Dolatabad Branch, Isfahan, Iran

3 Department of Mathematics, Persian Gulf University, Bushehr 75169-13817, Iran

Abstract

Let $G$ be a graph and $S(G)$ be the Seidel matrix of $G$. Let $s_1\ge s_2\ge \dots\ge s_n$ be the eigenvalues of $S(G)$. The spread of matrix $S(G)$ defined as  $s(G) := max_{i,j}|s_i-s_j| = s_1-s_n$. The Seidel energy of $G$, denoted by $SE(G)$, is defined to be the sum of the absolute value of all eigenvalues of the Seidel matrix of $G$. Willem Haemers conjectured that the Seidel energy of any graph with $n$ vertices is at least $2n-2$. Motivated by this conjecture, we prove that the conjecture is true if $s(G)\le n$. Moreover, we present some new bounds for the Seidel energy and also we study some properties of the Seidel eigenvalues of $G$.  Our results improve some known results.

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References

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Communications in Combinatorics and Optimization

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Available Online from 22 April 2026

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