Improved Bounds for the Extremal Non-Trivial Laplacian Eigenvalues

BÜYÜKKÖSE Ş., ALTINIŞIK E., Yalcin F.

GAZI UNIVERSITY JOURNAL OF SCIENCE, cilt.28, sa.1, ss.65-68, 2015 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 28 Sayı: 1
  • Basım Tarihi: 2015
  • Dergi Adı: GAZI UNIVERSITY JOURNAL OF SCIENCE
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.65-68
  • Gazi Üniversitesi Adresli: Evet

Özet

Let G be a simple connected graph and its Laplacian eigenvalues be mu(1) >= mu(2) >=...>= mu(n) = 0. In this paper, we present an upper bound for the algebraic connectivity mu(n=1) of G and a lower bound for the largest eigenvalue in terms of the degree sequence d(1,)d2,....d(n) and the number |N-i boolean AND N-j | of common vertices of i and j (1 <= i