A survey of the maximal and the minimal nullity in terms of omega invariant on graphs

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dc.contributor.authorOz, Mert Sinan
dc.contributor.authorCangul, Ismail Naci
dc.date.accessioned2026-02-12T21:05:42Z
dc.date.available2026-02-12T21:05:42Z
dc.date.issued2023
dc.departmentBursa Teknik Üniversitesi
dc.description.abstractLet 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.
dc.identifier.doi10.2478/ausm-2023-0019
dc.identifier.endpage353
dc.identifier.issn1844-6094
dc.identifier.issn2066-7752
dc.identifier.issue2
dc.identifier.scopus2-s2.0-85181715987
dc.identifier.scopusqualityQ2
dc.identifier.startpage337
dc.identifier.urihttps://doi.org/10.2478/ausm-2023-0019
dc.identifier.urihttps://hdl.handle.net/20.500.12885/7093
dc.identifier.volume15
dc.identifier.wosWOS:001135873700004
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSciendo
dc.relation.ispartofActa Universitatis Sapientiae-Mathematica
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WoS_20260212
dc.subjectnullity
dc.subjectmaximal nullity condition
dc.subjectminimal nullity condition
dc.subjectomega invariant
dc.subjectmatching number
dc.titleA survey of the maximal and the minimal nullity in terms of omega invariant on graphs
dc.typeArticle

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