On the least Q-eigenvalue of a non-bipartite hamiltonian graph

Least $Q$-eigenvalues of nonbipartite 2-connected graphs

“…Lemma 2.3 [15] Let n be an odd positive integer, G be a nonbipartite Hamiltonian graph of order n. Then q(G) ≥ q(C n ). Moreover, if the equality holds, then G ∼ = C n or G ∼ = H(i 1 , .…”

Further results on the least Q-eigenvalue of a graph with fixed domination number

“…Fan investigated q min of a graph under some perturbations, and minimized q min among the connected graphs with fixed order which contains a given nonbipartite graph as an induced subgraph. Recently, in [14], the authors determined all non-bipartite hamiltonian graphs whose q min attains the minimum.…”