On the first Zagreb index and multiplicative Zagreb coindices of graphs
| Autor: | A. Sinan Çevik, I. Naci Cangul, Muge Togan, Aysun Yurttas, Nihat Akgüneş, Kinkar Ch. Das |
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| Přispěvatelé: | Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü., Togan, Müge, Yurttaş, Aysun, Cangül, İsmail Naci, AAG-8470-2021, ABA-6206-2020, J-3505-2017, Selçuk Üniversitesi |
| Rok vydání: | 2016 |
| Předmět: |
Degree (graph theory)
010102 general mathematics Multiplicative function Eccentric connectivity index First and second multiplicative Zagreb coindex 01 natural sciences Graph Vertex (geometry) 010101 applied mathematics Combinatorics Unicyclic Graph Vertex Degree Narumi-Katayama index General Materials Science First Zagreb index 0101 mathematics Mathematics Mathematics applied Molecular-orbitals |
| Zdroj: | Analele Universitatii "Ovidius" Constanta - Seria Matematica. 24:153-176 |
| ISSN: | 1844-0835 |
| DOI: | 10.1515/auom-2016-0008 |
| Popis: | WOS: 000374768100008 For 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. National 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-Programme The 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. |
| Databáze: | OpenAIRE |
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