Comparing Zagreb indices for connected graphs
نویسندگان
چکیده
منابع مشابه
Comparing Zagreb indices for connected graphs
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...
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The first and the second Zagreb indices of a graph G = (V,E) are defined as M1(G) = ∑ u∈V dG(u) 2 and M2(G) = ∑ uv ∈ EdG(u)dG(v), where dG(u) denotes the degree of a vertex u in G. It has recently been conjectured that M1(G)/|V | ≤ M2(G)/|E|. Although some counterexamples have already been found, the question of characterizing graphs for which the inequality holds is left open. We show that thi...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2010
ISSN: 0166-218X
DOI: 10.1016/j.dam.2010.02.013