A note on the Bollobás-Nikiforov conjecture

• Published in: Linear algebra and its applications Vol. 710; pp. 230 - 242
• Main Authors: Zeng, Jiasheng, Zhang, Xiao-Dong
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2025
• Subjects: Adjacency matrix; Bollobás-Nikiforov conjecture; Eigenvalues of graph; Line graph; Triangle; Line graph; 05C50; Triangle; Adjacency matrix; Bollobás-Nikiforov conjecture; 05C35; Eigenvalues of graph

Bollobás and Nikiforov [2] proposed a conjecture that for any non-complete graph G with m edges and clique number ω, the following inequality holds:λ12+λ22≤2(1−1ω)m, where λ1 and λ2 are the two largest eigenvalues of the adjacency matrix A(G). Later, Elphick, Linz, and Wocjan [6] proposed a generali...