Abstract

The edge blow-up of a graph G, denoted by Gp+1, is obtained by replacing each edge of G with a clique of order p+1, where the new vertices of the cliques are all distinct. Yuan (2022) [20] determined the range of the Turán numbers for edge blow-up of all bipartite graphs and the exact Turán numbers for edge blow-up of all non-bipartite graphs. In this paper, we prove that the graphs with the maximum spectral radius in an n-vertex graph without any copy of edge blow-up of star forests are the extremal graphs for edge blow-up of star forests when n is sufficiently large.

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