Laplacian Spectra of Semigraphs

2023/07/06 by Pralhad Shinde, Shinde, Pralhad M.
Chemistry · Computer Science · Mathematics · #05C15 #05C99 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.2307.03209

openalex publication_date 2023/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a semigraph G=(V, E); in this paper, we study the eigenvalues of the Laplacian matrix of G. We show that the Laplacian of G is positive semi-definite, and G is connected if and only if λ₂ >0. Along the similar lines of graph theory bounds on the largest eigenvalue, we obtain upper and lower bounds on the largest Laplacian eigenvalue of G and enumerate the Laplacian eigenvalues of some special semigraphs such as star semigraph, rooted 3-uniform semigraph tree.

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