2019/07/11 by Nair Maria Maia de Abreu, de Abreu, Nair Maria Maia, Cláudia Marcela Justel +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.1907.04979
openalex publication_date 2019/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, structural properties of chordal graphs are analysed, in order to establish a relationship between these structures and integer Laplacian eigenvalues. We present the characterization of chordal graphs with equal vertex and algebraic connectivities, by means of the vertices that compose the minimal vertex separators of the graph; we stablish a sufficient condition for the cardinality of a maximal clique to appear as an integer Laplacian eigenvalue. Finally, we review two subclasses of chordal graphs, showing for them some new properties.