Identifying the graph with maximum or minimum spectral radius among a given class of graphs is a central problem in extremal spectral graph theory, known as the Brualdi- Solheid problem. For a graph G = (V-G, E-G), a subset S subset of V-G is called a maximum dissociation set if the induced subgraph G[S] does not contain P-3 as its subgraph, and the subset has maximum cardinality. The dissociation number of G is the number of vertices in a maximum dissociation set of G. In this paper, we first characterize all the connected graphs (resp. bipartite graphs, trees) having maximum spectral radius ...
