Bounds on the Second Stage Spectral Radius of Graphs

Let G be a graph of order n. The second stage adjacency matrix of G is the symmetric n × n matrix for which the ijth entry is 1 if the vertices vi and vj are of distance two; otherwise 0. The sum of the absolute values of this second stage adjacency matrix is called the second stage energy of G. In this paper we investigate a few properties and determine some upper bounds for the largest eigenvalue.

• S.K.Ayyaswamy
• S.Balachandran
• K.Kannan

• Second stage spectral radius
• Irreducible matrix
• Derived graph

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