# Laplacian Spectra of Kneser-Like Bipartite Graphs

#### Abstract

Given a,b ∈ N such that a > b we deﬁne a Kneser-like bipartite graph G(a, b), whose two bipartite sets of vertices represent the a-subsets and b-subsets of S = {1,...,a + b + 1}, and whose edges are pairs of vertices X and Y such that X ∩ Y = ∅. We prove that the eigenvalues of the Laplacian matrix of graphs G(a, 1) are all nonnegative integers. In fact, we describe these eigenvalues, and their respective multiplicities.

#### Subject Area

Mathematics

#### Recommended Citation

Vazquez, Cesar, "Laplacian Spectra of Kneser-Like Bipartite Graphs" (2020). *ETD Collection for University of Texas, El Paso*. AAI27995821.

https://scholarworks.utep.edu/dissertations/AAI27995821