On the first Zagreb index and multiplicative Zagreb coindices of graphs

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dc.contributor.authorDas, Kinkar Ch
dc.contributor.authorAkgüneş, Nihat
dc.contributor.authorTogan, Müge
dc.contributor.authorYurttaş, Aysun
dc.contributor.authorCangül, I. Naci
dc.contributor.authorÇevik, A. Sinan
dc.date.accessioned2020-03-26T19:25:28Z
dc.date.available2020-03-26T19:25:28Z
dc.date.issued2016
dc.departmentSelçuk Üniversitesien_US
dc.description.abstractFor a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as M-1(G) = Sigma v(i is an element of V(G))d(C)(v(i))(2), where d(G) (v(i)) is the degree of vertex v(i), in G. Recently Xu et al. introduced two graphical invariants (Pi) over bar (1) (G) = Pi v(i)v(j is an element of E(G)) (dG (v(i))+dG (v(j))) and (Pi) over bar (2)(G) = Pi(vivj is an element of E(G)) (dG (v(i))+dG (v(j))) named as first multiplicative Zagreb coindex and second multiplicative Zagreb coindex, respectively. The Narumi-Katayama index of a graph G, denoted by NK(G), is equal to the product of the degrees of the vertices of G, that is, NK(G) = Pi(n)(i=1) d(G) (v(i)). The irregularity index t(G) of G is defined as the num=1 ber of distinct terms in the degree sequence of G. In this paper, we give some lower and upper bounds on the first Zagreb index M-1(G) of graphs and trees in terms of number of vertices, irregularity index, maximum degree, and characterize the extremal graphs. Moreover, we obtain some lower and upper bounds on the (first and second) multiplicative Zagreb coindices of graphs and characterize the extremal graphs. Finally, we present some relations between first Zagreb index and NarumiKatayama index, and (first and second) multiplicative Zagreb index and coindices of graphs.en_US
dc.description.sponsorshipNational Research Foundation - Korean governmentKorean Government [2013R1A1A2009341]; Research Project Office of N. Erbakan University; Research Project Office of Uludag UniversityUludag University; Research Project Office of Selcuk UniversitySelcuk University; TUBITAK 2221-Programmeen_US
dc.description.sponsorshipThe first author is supported by the National Research Foundation funded by the Korean government with the grant no. 2013R1A1A2009341. The other authors are partially supported by Research Project Offices of N. Erbakan, Uludag and Selcuk Universities. This paper has been prepared during the Kinkar Ch. Das's visit in Turkey that was partially funded by TUBITAK 2221-Programme.en_US
dc.identifier.doi10.1515/auom-2016-0008en_US
dc.identifier.endpage176en_US
dc.identifier.issn1224-1784en_US
dc.identifier.issn1844-0835en_US
dc.identifier.issue1en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage153en_US
dc.identifier.urihttps://dx.doi.org/10.1515/auom-2016-0008
dc.identifier.urihttps://hdl.handle.net/20.500.12395/33852
dc.identifier.volume24en_US
dc.identifier.wosWOS:000374768100008en_US
dc.identifier.wosqualityQ4en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherOVIDIUS UNIV PRESSen_US
dc.relation.ispartofANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICAen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.selcuk20240510_oaigen_US
dc.subjectFirst Zagreb indexen_US
dc.subjectFirst and Second multiplicative Zagreb coindexen_US
dc.subjectNarumi-Katayama indexen_US
dc.titleOn the first Zagreb index and multiplicative Zagreb coindices of graphsen_US
dc.typeArticleen_US

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