For a graph, the least signless Laplacian eigenvalue is the least eigenvalue of its signless Laplacian matrix. This paper investigates how the least signless Laplacian eigenvalue of a graph changes under some perturbations, and minimizes the least signless Laplacian eigenvalue among all the nonbipartite graphs with given matching number and edge cover number, respectively.

For a graph, the least signless Laplacian eigenvalue is the least eigenvalue of its signless Laplacian matrix. This paper investigates how the least signless Laplacian eigenvalue of a graph changes under some perturbations, and minimizes the least signless Laplacian eigenvalue among all the nonbipartite graphs with given matching number and edge cover number, respectively.

We describe a necessary condition for zero-eigenvalue Turing instability, i.e., Turing instability arising from a real eigenvalue changing sign from negative to positive, for general chemical reaction networks modeled with mass-action kinetics. The reaction mechanisms are represented by the species-reaction graph (SR graph), which is a bipartite graph with different nodes representing species a...

We consider testing graph expansion in the bounded-degree graph model. Specifically, we refer to algorithms for testing whether the graph has a second eigenvalue bounded above by a given threshold or is far from any graph with such (or related) property. We present a natural algorithm aimed towards achieving the foregoing task. The algorithm is given a (normalized) eigenvalue bound λ < 1, oracl...

In this note we prove lower bounds on the components of the eigenvector associated with the dominant eigenvalue of a graph. These bounds depend only on the eccentricity of the corresponding node and on the eigenvalue As corrollary lower bounds on the dominant eigenvalue are derived, which depend on the diameter of the graph. These bounds were motivated by a heuristic algorithm for finding perip...

A quasi-symmetric design (QSD) is a (v, k, λ) design with two intersection numbers x, y, where 0 ≤ x < y < k. The block graph of a QSD is a strongly regular graph (SRG), whereas the converse is not true. Using Neumaier’s classification of SRGs related to the smallest eigenvalue, a complete parametric classification of QSDs whose block graph is an SRG with smallest eigenvalue −3, or second large...

In this paper we get a structural property for a graph having the minimal least eigenvalue among all graphs of fixed order and given chromatic number, and characterize such graphs under the condition that the chromatic number is not larger than half the order of the graph. As a result, we obtain a lower bound on the least eigenvalue in terms of the chromatic number, and an upper bound on the ch...