A note on the Turán number of disjoint union of wheels

Abstract The Turan number of a graph H, 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 m W 2 k + 1 ( k ≥ 3 ) denote the graph defined by taking m vertex disjoint copies of W 2 k + 1 . For sufficiently large n, we determine the Turan number and all extremal graphs for m W 2 k + 1 ( k ≥ 3 ). Let W h be the family of graphs obtain by the disjoint union of a finite number of wheels, such that, the number of even wheels in the union is h, ( h ≥ 1 ) . For any W ∈ W h , we also provide the Turan number and all extremal graphs for W, when n is sufficiently large.