Spectral Turán problem for [formula omitted]-free signed graphs

Abstract

The classical spectral Turán problem is to determine the maximum spectral radius of an F-free graph of order n. Let Kk− be the set of all unbalanced Kk. Wang, Hou and Li [25] and Chen and Yuan [10] studied the existence of unbalanced K3 and K4, respectively. In this paper, we focus on the spectral Turán problem of Kk−-free signed graph for k≥5. By using a different method, we give an answer for k=5 and completely characterize the corresponding extremal signed graph.