The least eigenvalues of signless Laplacian of non-bipartite graphs with pendant vertices

TL;DR

This paper identifies extremal non-bipartite graphs with pendant vertices that minimize or maximize the least eigenvalue of their signless Laplacian, establishing bounds based on pendant vertex count.

Contribution

It determines the graphs that achieve extremal least eigenvalues of the signless Laplacian among non-bipartite graphs with fixed order and pendant vertices, providing bounds.

Findings

Identified graphs with minimum and maximum least signless Laplacian eigenvalues.

Established bounds for the least eigenvalue based on pendant vertices.

Characterized extremal graphs in the specified class.

Abstract

In this paper we determine the graph whose least eigenvalue of signless Laplacian attains the minimum or maximum among all connected non-bipartite graphs of fixed order and given number of pendant vertices. Thus we obtain a lower bound and an upper bound for the least eigenvalue of signless Laplacian of a graph in terms of the number of pendent vertices.