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

• Veröffentlicht in: Algebra and Discrete Mathematics
• Datum: 2017
• 1. Verfasser: Oboudi, M.R.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2017
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/156636
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: On the difference between the spectral radius and the maximum degree of graphs / M.R. Oboudi // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 2. — С. 302-307. — Бібліогр.: 17 назв. — англ.

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...