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On the first Zagreb index and multiplicative Zagreb coindices of graphs

2016; Ovidius University; Volume: 24; Issue: 1 Linguagem: Inglês

10.1515/auom-2016-0008

1844-0835

Kinkar Chandra Das, Nihat Akgüneş, Müge Togan, Aysun Yurttaş, İsmail Naci Cangül, A. Sinan Çevik,

Synthesis and Properties of Aromatic Compounds

Abstract For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as , where d G (v i ) is the degree of vertex vi in G. Recently Xu et al. introduced two graphical invariants and 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) = . The irregularity index t(G) of G is defined as the number of distinct terms in the degree sequence of G. In this paper, we give some lower and upper bounds on the first Zagreb index M1(G) of graphs and trees in terms of number of vertices, irregularity index, maxi- mum 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 Narumi-Katayama index, and (first and second) multiplicative Zagreb index and coindices of graphs.