On the spectral Turan problem of theta graphs

In 2010, Nikiforov conjectured that for l >= 2 and n sufficiently large, S-n,l - 1(1) is the unique graph with the maximum spectral radius over all n - vertex C (2l) -free graphs. In 2022, Cioaba, Desai and Tait solved this conjecture. The theta graph e t, consists of two vertices joined by t vertex -disjoint paths, each of length t. Particularly, Theta(2,l) congruent to C-2l . In this paper, we characterize the unique extremal graph which attains the maximum spectral radius among all Theta(t,l)-free graphs of order n, where t,l >= 3 and n is sufficiently large. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.