On bounds for the index of double nested graphs

The index of a simple graph is the largest eigenvalue of its adjacency matrix. It is well-known that in the set of all connected graphs with fixed order and size the graphs with maximal index are nested split graphs. It was recently observed that double nested graphs assume the same role if we restrict ourselves to bipartite graphs. In this paper we provide some bounds (lower and upper) for the index of double nested graphs. Some computational results are also included.