2023/03/15 by Hiranya Kishore Dey, Dey, Hiranya Kishore, Soumyajit Saha +1
Chemistry · Computer Science · Mathematics · #05C50 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Metal-Organic Frameworks: Synthesis and Applications #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2303.08417
openalex publication_date 2023/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Urschel introduced a notion of nodal partitioning to prove an upper bound on the number of nodal decomposition of discrete Laplacian eigenvectors. The result is an analogue to the well-known Courant's nodal domain theorem on continuous Laplacian. In this article, using the same notion of partitioning, we discuss the lower bound (or lack thereof) on the number of nodal decomposition of eigenvectors in the class of all graphs with a fixed number of vertices (however large). This can be treated as a discrete analogue to the results of Stern and Lewy in the continuous Laplacian case.