Spectral extremal graphs for edge blow-up of star forests.

The edge blow-up of a graph G , denoted by G p + 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. [ABSTRACT FROM AUTHOR]