On the difference between the spectral radius and the maximum degree of graphs

• Main Author: Oboudi, M.R.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2017
• Series: Algebra and Discrete Mathematics
• Online Access: http://dspace.nbuv.gov.ua/handle/123456789/156636

Let G be a graph with the eigenvalues λ₁(G)≥⋯≥λn(G). The largest eigenvalue of G, λ₁(G), is called the spectral radius of G. Let β(G)=Δ(G)−λ₁(G), where Δ(G) is the maximum degree of vertices of G. It is known that if G is a connected graph, then β(G)≥0 and the equality holds if and only if G is regu...