Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph....

‎let g=(v,e) be a simple connected graph with vertex set v and edge set e. the first, second and third zagreb indices of g are respectivly defined by: $m_1(g)=sum_{uin v} d(u)^2, hspace {.1 cm} m_2(g)=sum_{uvin e} d(u).d(v)$ and $ m_3(g)=sum_{uvin e}| d(u)-d(v)| $ , where d(u) is the degree of vertex u in g and uv is an edge of g connecting the vertices u and v. recently, the first and second m...

the first zagreb index $m_1$ of a graph $g$ is equal to the sum of squaresof degrees of the vertices of $g$. goubko proved that for trees with $n_1$pendent vertices, $m_1 geq 9,n_1-16$. we show how this result can beextended to hold for any connected graph with cyclomatic number $gamma geq 0$.in addition, graphs with $n$ vertices, $n_1$ pendent vertices, cyclomaticnumber $gamma$, and minimal $m...

Todeschini et al. have recently suggested to consider multiplicative variants of additive graph invariants, which applied to the Zagreb indices would lead to the multiplicative Zagreb indices of a graph G, denoted by ( ) 1  G and ( ) 2  G , under the name first and second multiplicative Zagreb index, respectively. These are define as     ( ) 2 1 ( ) ( ) v V G G G d v and ( ) ( ) ( ) ( ) 2...

Abstract Analogues to multiplicative Zagreb indices in this paper two new type of eccentricity related topological index are introduced called the first and second multiplicative Zagreb eccentricity indices and is defined as product of squares of the eccentricities of the vertices and product of product of the eccentricities of the adjacent vertices. In this paper we give some upper and lower b...

Let G be a graph. In this paper, we study the eccentric connectivity index, the new version of the second Zagreb index and the forth geometric–arithmetic index.. The basic properties of these novel graph descriptors and some inequalities for them are established.

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...

For a graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Denote by Gn,k the set of graphs with n vertices and k cut edges. In this paper, we showed the types of graphs with the largest and the second largest M1 and M2 among Gn,k .

For a nontrivial graph G, its first Zagreb coindex is defined as the sum of degree sum over all non-adjacent vertex pairs in G and the second Zagreb coindex is defined as the sum of degree product over all non-adjacent vertex pairs in G. Till now, established results concerning Zagreb coindices are mainly related to composite graphs and extremal values of some special graphs. The existing liter...