[PDF] Top 20 On the first variable Zagreb index

... The first variable Zagreb index of graph G is defined as ( ) = ∑ ∈ ( ) ( ) , where  is a real number and d(v) is the degree of vertex ...this index in random increasing trees ... See full document

... [7] X. L. Li, I. Gutman, Mathematical Aspects of Randić-Type Molecular Structure Descriptors, Mathematical Chemistry Monograph 1, University of Kragujevac, 2006. [8] S. Nikolić, G. Kovačević, A. Miličević, N. Trinajstić, ... See full document

... Proof. Let n = 2r + 1. There are four kind of edges in L. The vertices of the first kind of edges have degree n 2 + 1 = r + 1 and and the reverse degree of these vertices are r + 1. The vertices of the second kind ... See full document

... the first general Zagreb index of G as follows ( ) = ∑ ∈ ( ) ( ) ...the first three smallest and largest values of the first general Zagreb index, where α is an integer or ... See full document

... In this section, we focus on the structure of hydrocarbon structures and counting the First Multiple Zagreb index and Second Multiple Zagreb index of Polycyclic Aromatic Hydrocarbons ... See full document

... modified first and second Zagreb indices, harmonic index and augmented Zagreb index for certain networks like silicate networks and honeycomb ... See full document

... Throughout this paper graph means simple connected graphs. Let G be a connected graph with vertex and edge sets V(G) and E(G), respectively. As usual, the degree of a vertex u of G is denoted by deg(u) and it is defined ... See full document

... Let G be simple graph. The first Zagreb index is the sum of squares of degree of vertices and second Zagreb index is the sum of the products of the degrees of pairs of[r] ... See full document

... topological index is a numeric quantity from the structural graph of a ...compute first multiplicative Zagreb index, multiplicative hyper-Zagreb, general multiplicative Zagreb, ... See full document

... In 1975, Milan Randi´c [16] proposed a structural descriptor, based on the end-vertex degrees of edges in a graph, called the branching index that later became the well-known Randi´c connectivity index. The ... See full document

... the first reformulated Zagreb index of graphs with connectivity at most k and characterized the corresponding extremal ...on Zagreb and reformulated Zagreb indices of simple ... See full document

... the first Zagreb index as the Multiplicative Zagreb Eccentricity index that introduced by Nilanjan De and ε(u) is the largest distance between u and any other vertex v of ...topological ... See full document

... leap Zagreb indices and studied their ...the first leap Zagreb index of some graph operations ...computed first leap Zagreb index of some nano ...leap Zagreb ... See full document

... topological index namely, forgotten topological index and it is clearly stated that the forgotten index is a special case of the earlier much studied general first Zagreb ...F– ... See full document

... HyperZagreb index. Example 1. In this example the HyperZagreb index of some well-known graphs are ...We first consider the complete graph K n ... See full document

... irr(G) = ∑ ∈ ( ) |d (u) − d (v)| (1) In [6], Albertson gave some upper bounds on irregularity for trees, bipartite, and triangle-free graphs. Recall that the first Zagreb index M and the second ... See full document

... topological index or molecular structure ...reformulated first Zagreb index and the fifth arithmetic- geometric index of triangular benzenoid T n and hexagonal parallelogram P(m,n) ... See full document

... the first hyper-Zagreb index in the set of all connected tricyclic ...graphs. First we intro- duced the transformations which strictly increases the first hyper-Zagreb ... See full document

... Over the time, the multiplicative versions of the indices were also defined. Todeschini et al. [18] who introduced the multiplicative counterparts of the additive invariants of a graph lead to the definition of ... See full document

... Randić index, inverse Randić index, first and second Zagreb index, modified Zagreb index, Symmetric division index, Inverse sum index augmented Zagreb ... See full document