The Tur\'an number of a graph $H$, $\text{ ex}(n,H)$, is the maximum number of edges in a graph on $n$ vertices which does not have $H$ as a subgraph. A wheel $W_n$ is an $n$-vertex graph formed by connecting a single vertex to all vertices of a cycle $C_{ n-1}$. Let $mW_{ 2k+1}$ denote the $m$ vertex-disjoint copies of $W_{ 2k+1}$. For sufficiently large $n$, we determine the Tur\'an number and all extremal graphs for $mW_{ 2k+1}$. We also provide the Tur\'an number and all extremal graphs for $W^{ h}:=\bigcup\limits^m_{ i=1}W_{ k_i}$ when $n$ is sufficiently large, where the number of even wheels is $h$ and $h>0$.
Categories: math.CO