Nonregular graphs with a given maximum degree attaining the maximum spectral radius

Let G be a connected nonregular graphs of order n with maximum degree k that attains the maximum spectral radius. In 2008, Liu and Li proposed a conjecture stating that G has a degree sequence (k,…,k,t) with t=k-1 or k-2. In this talk, I will present some progress on this conjecture. This talk is based on joint work with Jiahui Liu and Chenxi Yang.