let $g$ be a graph and let $m_{ij}(g)$, $i,jge 1$, be the number of edges $uv$ of $g$ such that ${d_v(g), d_u(g)} = {i,j}$. the {em $m$-polynomial} of $g$ is introduced with $displaystyle{m(g;x,y) = sum_{ile j} m_{ij}(g)x^iy^j}$. it is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular ca...

topological indices are numerical parameters of a graph which characterize its topology. inthis paper the pi, szeged and zagreb group indices of the tetrameric 1,3–adamantane arecomputed.

‎The first multiplicative Zagreb index $Pi_1(G)$ is equal to the‎ ‎product of squares of the degree of the vertices and the second‎ ‎multiplicative Zagreb index $Pi_2(G)$ is equal to the product of‎ ‎the products of the degree of pairs of adjacent vertices of the‎ ‎underlying molecular graphs $G$‎. ‎Also‎, ‎the multiplicative sum Zagreb index $Pi_3(G)$ is equal to the product of‎ ‎the sum...

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...

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....

in this paper we study the zagreb index in bucket recursive trees containing buckets with variable capacities. this model was introduced by kazemi in 2012. weobtain the mean and variance of the zagreb index andintroduce a martingale based on this quantity.

in this paper, the degree distance and the gutman index of the corona product of two graphs are determined. using the results obtained, the exact degree distance and gutman index of certain classes of graphs are computed.

The Zagreb eccentricity indices are the eccentricity reformulation of the Zagreb indices. Let H be a simple graph. The first Zagreb eccentricity index (E1(H)) is defined to be the summation of squares of the eccentricity of vertices, i.e., E1(H) = ∑u∈V(H) Symmetry 2016, 9, 7; doi: 10.3390/sym9010007 www.mdpi.com/journal/symmetry Article First and Second Zagreb Eccentricity Indices of Thorny Gra...

Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg1(G,x) and Zg1(G) of the graph G are defined as ( ) ( ) ∑ u v u d v E G d x + ∈ and ( ) ( ) ∑ e u G v uv E d d = ∈ + respectively. Recently Ghorbani and Hosseinzadeh introduced the first Eccentric Z...