Turán numbers for odd wheels

The Turán number ex(n,G) is the maximum number of edges in any n-vertex graph that does not contain a subgraph isomorphic to G. A wheelWn is a graph on n vertices obtained from a Cn−1 by adding one vertex w and making w adjacent to all vertices of the Cn−1. We obtain two exact values for small wheels: ex(n,W5)=⌊n24+n2⌋,ex(n,W7)=⌊n24+n2+1⌋.Given that ex(n,W6) is already known, this paper completes the spectrum for all wheels up to 7 vertices. In addition, we present the construction which gives us the lower bound ex(n,W2k+1)>⌊n24⌋+⌊n2⌋ in general case.