For a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M2 is equal to the sum of products of degrees of pairs of adjacent vertices. In this paper, we study the Zagreb indices of n-vertex connected graphs with k cut vertices, the upper bound for M1and M2-values of n-vertex connected graphs with k cut vertices are deter...

Applications in chemistry motivated mathematicians to define different topological indices for types of graphs. The Hyper-Zagreb index (HM) is an important tool as it integrates the first and second Zagreb indices. In this paper, we characterize trees unicyclic graphs with four eight greatest HM-value, respectively.

let $g$ be a connected graph. the multiplicative zagreb eccentricity indices of $g$ are defined respectively as ${bf pi}_1^*(g)=prod_{vin v(g)}varepsilon_g^2(v)$ and ${bf pi}_2^*(g)=prod_{uvin e(g)}varepsilon_g(u)varepsilon_g(v)$, where $varepsilon_g(v)$ is the eccentricity of vertex $v$ in graph $g$ and $varepsilon_g^2(v)=(varepsilon_g(v))^2$. in this paper, we present some bounds of the multi...

In this note, we give expressions for the first(second) Zagreb coindex, second Zagreb index(coindex), third Zagreb index and first hyper-Zagreb index of the line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p, q] and obtain upper bounds for Wiener index and degree-distance index of these graphs. This note continue the program of computing certain topological indi...

a topological index of a molecular graph g is a numeric quantity related to g which isinvariant under symmetry properties of g. in this paper we obtain the randić, geometricarithmetic,first and second zagreb indices , first and second zagreb coindices of tensorproduct of two graphs and then the harary, schultz and modified schultz indices of tensorproduct of a graph g with complete graph of ord...

The multiplicative sum Zagreb index is defined for a simple graph G as the product of the terms dG(u)+dG(v) over all edges uv∈E(G) , where dG(u) denotes the degree of the vertex u of G . In this paper, we present some lower bounds for the multiplicative sum Zagreb index of several graph operations such as union, join, corona product, composition, direct product, Cartesian product and strong pro...

let g be a simple connected graph. the first and second zagreb indices have been introducedas  vv(g)(v)2 m1(g) degg and m2(g)  uve(g)degg(u)degg(v) , respectively,where degg v(degg u) is the degree of vertex v (u) . in this paper, we define a newdistance-based named hyperzagreb as e uv e(g) .(v))2 hm(g)     (degg(u)  degg inthis paper, the hyperzagreb index of the cartesian product...