“…Inequality (3) impulsed the great interests of studying the maximum spectral radius for F -free graphs with given number of edges, see [32,35] for K r+1 -free graphs, [34,50,46] for C 4 -free graphs, [49] for K 2,r+1 -free graphs, [49,31] for C 5 -free or C 6 -free graphs, [29] for C 7 -free graphs, [43,9,26] for C △ 4 -free or C △ 5 -free graphs, where C △ k is a graph on k + 1 vertices obtained from C k and C 3 by sharing a common edge; see [37] for B k -free graphs, where B k denotes the book graph consisting of k triangles sharing a common edge, [21] for F 2 -free graphs with given number of edges, where F 2 is the friendship graph consisting of two triangles intersecting in a common vertex, [38,39] for counting the number of C 3 and C 4 . We refer the readers to the surveys [36,18] and references therein.…”