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New bounds for Seidel energy of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 اردیبهشت 1405 اصل مقاله (390.04 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30809.2627 | ||
| نویسندگان | ||
| Mohammad Reza Oboudi* 1؛ Akbar Jahanbani2؛ Reza Sharafdini3 | ||
| 1Department of Mathematics, College of Science, Shiraz University, Shiraz, Iran | ||
| 2Sama Technical and Vocational School, Dolatabad Branch, Isfahan, Iran | ||
| 3Department of Mathematics, Persian Gulf University, Bushehr 75169-13817, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Seidel energy of graphs؛ Haemers' s conjecture؛ Seidel eigenvalues | ||
| مراجع | ||
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