The Least Eigenvalue of the Graphs Whose Complements Are Connected and Have Pendent Paths

The adjacency matrix of a graph is a matrix which represents adjacent relation between the vertices of the graph. Its minimum eigenvalue is defined as the least eigenvalue of the graph. Let G_n be the set of the graphs of order n, whose complements are connected and have pendent paths. This paper investigates the least eigenvalue of the graphs and characterizes the unique graph which has the minimum least eigenvalue in G_n.