2024/04/14 by Aryan Esmailpour, Sara Saeedi Madani, Esmailpour, Aryan +3
Computer Science · Mathematics · #05C50 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2404.09268
openalex publication_date 2024/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a graph, and let λ(G) denote the smallest eigenvalue of G. First, we provide an upper bound for λ(G) based on induced bipartite subgraphs of G. Consequently, we extract two other upper bounds, one relying on the average degrees of induced bipartite subgraphs and a more explicit one in terms of the chromatic number and the independence number of G. In particular, motivated by our bounds, we introduce two graph invariants that are of interest on their own. Finally, special attention goes to the investigation of the sharpness of our bounds in various classes of graphs as well as the comparison with an existing well-known upper bound.