On the second minimizing graph in the set of complements of trees

Abstract

Let G be a graph of order n and A(G)=[ai,j]be its adjacency matrix such that ai,j=1 if viis adjacent to vjand ai,j=0 otherwise, where 1≤i,j≤n. In a certain family of graphs, a graph is called minimizing (or second minimizing) if the least eigenvalue of its adjacency matrix attains the minimum (or second minimum). In this paper, we characterize the second minimizing graph among all graphs which belong to the set of complements of the trees. Keywords: Adjacency matrix, Least eigenvalue, Complement of trees