نتایج جستجو برای Zagreb indices

تعداد نتایج: 53995  

2006
P. Hansen, D. Vukicević, Pierre Hansen, Damir Vukicević,

Let G = (V,E) be a simple graph with n = |V | vertices and m = |E| edges; let d1, d2, . . . , dn denote the degrees of the vertices of G. If ∆ = max i di ≤ 4, G is a chemical graph. The first and second Zagreb indices are defined as M1 = ∑

2013
Nilanjan De,

The reformulated Zagreb indices of a graph is obtained from the classical Zagreb by replacing vertex degree by edge degree and are defined as sum of squares of the degree of the edges and sum of product of the degrees of the adjacent edges. In this paper we give some explicit results for calculating the first and second reformulated Zagreb indices of dendrimers. Mathematics Subject Classificati...

2011
Ivan Gutman,

Let G be a graph with vertex set V (G) and edge set E(G) . The first and second multiplicative Zagreb indices of G are Π1 = ∏ x∈V (G) deg(x) 2 and Π2 = ∏ xy∈E(G) deg(x) deg(y) , respectively, where deg(v) is the degree of the vertex v . Let Tn be the set of trees with n vertices. We determine the elements of Tn , extremal w.r.t. Π1 and Π2 . AMS Mathematics Subject Classification (2000): 05C05, ...

2017
ZHONGZHU LIU, QINGHUA MA, YIZHI CHEN, Z. LIU, Q. MA,

The Zagreb indices are among the oldest and the most famous topological molecular structure-descriptors. The first Zagreb index is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index is equal to the sum of the products of the degrees of pairs of adjacent vertices of the respective graph. In this paper, we characterize the extremal graphs with maximal, sec...

Journal: :Discrete Applied Mathematics 2012
Hosam Abdo, Darko Dimitrov, Ivan Gutman,

For a simple graph G with n vertices and m edges, the first Zagreb index and the second Zagreb index are defined as M1(G) = ∑ v∈V d(v) 2 and M2(G) = ∑ uv∈E d(u)d(v). In [34], it was shown that if a connected graph G has maximal degree 4, then G satisfies M1(G)/n = M2(G)/m (also known as the Zagreb indices equality) if and only if G is regular or biregular of class 1 (a biregular graph whose no ...

2014
Nilanjan De,

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...

2015
Yun Gao, Wei Gao, Li Liang,

Chemical compounds and drugs are often modelled as graphs where each vertex represents an atom of molecule, and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is often called its molecular graph, and can be different structures. In this paper, by virtue of mathematical derivation, we determine the fourth, f...

M. GHORBANI, N. AZIMI,

The Zagreb indices are the oldest graph invariants used in mathematical chemistry to predict the chemical phenomena. In this paper we define the multiple versions of Zagreb indices based on degrees of vertices in a given graph and then we compute the first and second extremal graphs for them.

Journal: :Discrete Applied Mathematics 2010
Batmend Horoldagva, Sang-Gu Lee,

It was conjectured that for each simple graph G = (V , E) with n = |V (G)| vertices and m = |E(G)| edges, it holdsM2(G)/m ≥ M1(G)/n, whereM1 andM2 are the first and second Zagreb indices. Hansen and Vukičević proved that it is true for all chemical graphs and does not hold in general. Also the conjecture was proved for all trees, unicyclic graphs, and all bicyclic graphs except one class. In th...

2011
Damir Vukičević, Ivan Gutman, Boris Furtula, Vesna Andova, Darko Dimitrov,

Let G be a simple graph possessing n vertices and m edges. Let di be the degree of the i-th vertex of G , i = 1, . . . , n . The first Zagreb index M1 is the sum of d 2 i over all vertices of G . The second Zagreb index M2 is the sum di dj over pairs of adjacent vertices of G . In this paper we search for graph for which M1/n = M2/m , and show how numerous such graphs can be constructed. In add...

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