The least eigenvalue of graphs with given connectivity

A note on the least eigenvalue of a graph with given maximum degree

“…Wang and Fan [10] gave the graph of order n with k cut vertices having the minimal least eigenvalue. Ye et al [11] discussed the least eigenvalues of graphs with given connectivity. Zhu [12] also consider the least eigenvalues of graphs with cut vertices or edges.…”

Spectral conditions for the existence of specified paths and cycles in graphs

“…Let λ n (G) be the least eigenvalue of a graph G of order n. It is known that λ n (G) = −ρ(G) for a bipartite graph G (see [4]). Recently, researchers have begun to pay attention to the least eigenvalues of graphs with a given value of some well-known integer graph invariant: for instance: order and size [1,2,5,13], unicyclic graphs with a given number of pendant vertices [7], matching number and independence number [14], number of cut vertices [15], connectivity, chromatic number [16], domination number [17]. This paper also gives a spectral extremal characterization on the least eigenvalue of graphs (see Theorems 1.3 and 1.4).…”

Bound on the least eigenvalue of a graph with cut vertices

“…Spectral radius and the least eigenvalue were investigated in the literature for many classes of graphs; see, for example, [2][3][4] and [5][6][7][8][9][10][11][12][13][14][15], respectively. Let G k n be the set of the connected graphs with n-vertices and k-cut vertices.…”