Maximizing the Hamming Spectral Radius in Graphs

Let B(G) denote the incidence matrix of a simple connected graph G.The Hamming matrix H(G) of G is defined as the matrix whose entries are the Hamming distances between the binary strings derived from the rows of B(G).The spectral radius of H(G) is called the Hamming spectral radius of G.In this paper, we characterize the graphs that maximize the Hamming spectral radius among connected graphs of a given order under either of the following conditions: (i) exactly one vertex has degree greater than 2; (ii) exactly two vertices have degree greater than 2.