2019/04/10 by Huicai Jia, Hong‐Jian Lai, Jia, Huicai +5
Chemistry · Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems #Synthesis and Properties of Aromatic Compounds
paper · pdf · doi:10.48550/arxiv.1904.04970
openalex publication_date 2019/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let q(G) denote the Q-index of a graph G, which is the largest signless Laplacian eigenvalue of G. We prove best possible upper bounds of q(G) and best possible lower bounds of q(G) for a connected graph G to be k-connected and maximally connected, respectively. Similar upper bounds of q(G) and lower bounds of q(G) to assure G to be super-connected are also obtained. Upper bounds of q(G) and lower bounds of q(G) to assure a connected triangle-free graph G to be k-connected, maximally connected and super-connected are also respectively investigated.