Extremal Properties of the Zagreb Eccentricity Indices
نویسندگان
چکیده
منابع مشابه
On multiplicative Zagreb eccentricity indices
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...
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Let G be a connected graph. The multiplicative Zagreb eccentricity indices of G are defined respectively as Π1(G) = ∏ v∈V (G) ε 2 G(v) and Π ∗ 2(G) = ∏ uv∈E(G) εG(u)εG(v), where εG(v) is the eccentricity of vertex v in graph G and εG(v) = (εG(v)) . In this paper, we present some bounds of the multiplicative Zagreb eccentricity indices of Cartesian product graphs by means of some invariants of t...
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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...
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The eccentricity of a vertex is the maximum distance from it to another vertex and the average eccentricity ecc(G) of a graph G is the mean value of eccentricities of all vertices of G. The average eccentricity is deeply connected with a topological descriptor called the eccentric connectivity index, defined as a sum of products of vertex degrees and eccentricities. In this paper we analyze ext...
متن کاملNote on the comparison of the first and second normalized zagreb eccentricity indices.
The conjecture Σuv V(G) dG(u)2 / n(G) ≤ Σuvv E(G) dG(u)dG(v) / m(G) that compares normalized Zagreb indices attracted recently a lot of attention1-9. In this paper we analyze analogous statement in which degree dG(u) of vertex u is replaced by its eccentricity δG(u) in which way we define novel first and second Zagreb eccentricity indices. We show that Σuv V(G) εG(u)2 / n(G) ≥ Σuvv E(G) εG(u)εG...
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ژورنال
عنوان ژورنال: Croatica Chemica Acta
سال: 2012
ISSN: 0011-1643,1334-417X
DOI: 10.5562/cca2020