The ( k , r ) -fan is the graph consisting of copies complete K which intersect in a single vertex, and denoted by F . Erd?s et al. (1995) [14] determined maximum number edges an n -vertex that does not contain 3 as subgraph. Furthermore, Chen (2003) [5] proved analogous result on for general case ? In this paper, we show sufficiently large graphs order no copy attain spectral radius are also e...

Let A(n; k; t) denote the smallest integer e for which every k-connected graph on n vertices can be made (k + t)-connected by adding e new edges. We determine A(n; k; t) for all values of n; k and t in the case of (directed and undirected) edge-connectivity and also for directed vertex-connectivity. For undirected vertex-connectivity we determine A(n; k; 1) for all values of n and k. We also de...