On Turan number for Sl1 ∨ Sl2

The Turan number of a graph G, denoted by ex(n, G), is the maximum number of edges of an n-vertex simple graph having no G as a subgraph. Let S-l denote the star on l + 1 vertices. In this paper, we investigate to determine the Turan number for Sl(1) boolean OR Sl(2), where 1(l) > l(2). We give a new lower bound on ex(n, Sl(1) boolean OR Sl(2)). Moreover, if l(2) + 1 <= l(1) <= 2l(2) + 1 (or if l(1) >= 3 and l(2) = 2), we determine the exact values ex(n, Sl(1) boolean OR Sl(2)) for all positive integers n (or for almost all positive integers n), which improves two results of Lidickyet al. (C) 2020 Elsevier Inc. All rights reserved.