Minimizing graph of the connected graphs whose complements are bicyclic with two cycles

Abstract

In a certain class of graphs, a graph is called minimizing if the least eigenvalueof its adjacency matrix attains the minimum. A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. In this paper, we characterize the minimizinggraph among all the connected graphs that belong to a class of graphs whose complements are bicyclic with two cycles.