Let F denote a set of graphs. A graph G is said to be F-free if it does not contain any element of F as a subgraph. The Turan number is the maximum possible number of edges in an F-free graph with n vertices. It is well known that classical Turan type extremal problem aims to study the Turan number of fixed graphs. In 2010, Nikiforov [17] proposed analogously a spectral Turan type problem which asks to determine the maximum spectral radius of an F-free graph with n vertices. It attracts much attention and many such problems remained elusive open even after serious attempts, and so they are con...
