Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2025 07 20 Super spanning connectivity of the cartesian product of complete graphs 14995 10.22049/cco.2025.29249.1909 EN Xiaoqian Wang College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, P. R. China Eminjan Sabir College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, P. R. China Journal Article 2023 12 06 Let $G$ be a graph and $s$ be an integer. {\textit{A $s$-container $C(x,y)$} of $G$ between two vertices $x$ and $y$ is a set of $s$ internally vertex disjoint $x,y$-paths. A $s$-container $C(x,y)$ is \textit{a $s^{*}$-container} if $V(C(x,y))=V(G)$, where $V(C(x, y))$ is the set of vertices incident with some paths in $C(x,y)$. Then $G$ is \textit{$s^{*}$-connected} if there exists a $s^{*}$-container between any two distinct vertices of $G$. \textit{The spanning connectivity $\kappa^{*}(G)$} of $G$ is the largest integer $k$ such that $G$ is $s^{*}$-connected for any $s$ with $1 \leq s \leq k$. Further, $G$ is \textit{super spanning connected} if $\kappa^{*}(G)=\kappa(G)$, where $\kappa(G)$ is the connectivity of $G$. In this paper, we show that the $n$-th cartesian product of complete graph $K_{t}$ $(t\ge 3)$ is super spanning connected. Our results, in some sense, extended a previous result in \textit{[Shih et al., One-to-one disjoint path covers on $k$-ary $n$-cubes, Theoret. Comput. Sci. (2011)]}. https://comb-opt.azaruniv.ac.ir/article_14995_12c69f029b29ddf871c5d9bf82542d24.pdf