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Kinkar Ch. Das, Nihat Akgunes, Muge Togan, Aysun Yurttas, I. Naci Cangul and A. Sinan Cevik

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 dG(vi) 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.

Open access

V. Lokesha, R. Shruti and T. Deepika

Abstract

The molecular topological indices as validly demonstrated its high performance in the discovery and design of new drugs. The goal of this paper is to study the structurally constructed a graph model of human Liver using graph operator. After the construction, nurtured the model using various topological indices. Also, established a diagnosis defect in the human Liver. Basically, considered structure of Liver can divide into healthy Liver and affected Liver. In this case study the topological indices are used in describe the structure of Liver using graph operator. Constructed model can be useful further in the medical field for any diagnosis with special care.