University of Kashan Mathematics Interdisciplinary Research 2538-3639 11 3 2026 09 01 Secure Domination Number in Kneser Graph 243 251 115653 10.22052/mir.2026.258107.1562 EN Abolfazl Bahmani ‎Department of Mathematics, ‎University of Zanjan, ‎Zanjan‎, ‎I‎. ‎R‎. ‎Iran Saeid Alikhani ‎Department of Mathematical Sciences, ‎Yazd University, 89195-741‎, ‎Yazd‎, ‎I‎. ‎R‎. ‎Iran 0000-0002-1801-203X Journal Article 2025 12 09 ‎A vertex subset $S \subseteq V(G)$ is defined as a secure dominating set if‎, ‎for any vertex u outside of S‎, ‎there is a neighbor $v \in S$ such that the set $(S \setminus \{v\}) \cup \{u\}$ remains a dominating set for the graph $G$‎. ‎The minimum cardinality of such a set is termed the secure domination number and is denoted by $\gamma_s(G)$‎. ‎In the present study‎, ‎we establish specific bounds for the secure domination number of Kneser graphs K(n‎, ‎k)‎. ‎We further prove that for the condition $n \ge k^2‎ + ‎2k$‎, ‎the value of $\gamma_s(K(n‎, ‎k))$ is precisely k‎ + ‎2‎. https://mir.kashanu.ac.ir/article_115653_6ea992752c5e0704d705b3842909eba3.pdf