A survey of the maximal and the minimal nullity in terms of omega invariant on graphs
Küçük Resim Yok
Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Sciendo
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Let G = (V, E) be a simple graph with n vertices and m edges. nu(G) and c(G) = m - n + theta be the matching number and cyclomatic number of G, where theta is the number of connected components of G, respectively. Wang and Wong in [18] provided formulae for the upper and the lower bounds of the nullity eta(G) of G as eta(G) = n - 2 nu(G) + 2c(G) and eta(G) = n - 2 nu(G) - c(G), respectively. In this paper, we restate the upper and the lower bounds of nullity eta(G) of G utilizing omega invariant and inherently vertex degrees of G. Also, in the case of the maximal and the minimal nullity conditions are satisfied for G, we present both two main inequalities and many inequalities in terms of Omega invariant, analogously cyclomatic number, number of connected components and vertex degrees of G.
Açıklama
Anahtar Kelimeler
nullity, maximal nullity condition, minimal nullity condition, omega invariant, matching number
Kaynak
Acta Universitatis Sapientiae-Mathematica
WoS Q Değeri
Q3
Scopus Q Değeri
Q2
Cilt
15
Sayı
2
