ZAGREB ALLIANCE INDICES

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چکیده

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Comparing the Zagreb Indices

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 = ∑

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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...

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On the Zagreb Indices Equality

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 ...

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ژورنال

عنوان ژورنال: Advances in Mathematics

سال: 2021

ISSN: ['1857-8365', '1857-8438']

DOI: https://doi.org/10.37418/amsj.10.3.15