The sharp bounds of Zagreb indices on connected graphs
نویسندگان
چکیده
منابع مشابه
Sharp lower bounds for the Zagreb indices of unicyclic graphs
The first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices of the respective graph. In this paper we present the lower bound on M1 and M2 among all unicyclic graphs of given order, maximum degree, and cycle length, and characterize graphs for which th...
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For a (molecular) graph, the multiplicative Zagreb indices ∏ 1-index and ∏ 2index are multiplicative versions of the ordinary Zagreb indices (M1-index and M2index). In this note we report several sharp upper bounds for ∏ 1-index in terms of graph parameters including the order, size, radius, Wiener index and eccentric distance sum, and upper bounds for ∏ 2-index in terms of graph parameters inc...
متن کاملComparing 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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A bound on the values of independence polynomials at-1/k for k-degenerate graphs", Discrete Mathematics 2013 (To appear) Estes, Staton, Wei. " A bound on the values of independence polynomials at-1/k for k-degenerate graphs " Discrete Mathematics.
متن کاملSharp upper bounds on Zagreb indices of bicyclic graphs with a given matching number
For a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M2 is equal to the sum of products of degrees of pairs of adjacent vertices. In this paper, we investigate Zagreb indices of bicyclic graphs with a given matching number. Sharp upper bounds for the first and second Zagreb indices of bicyclic graphs in terms of the...
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ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2021
ISSN: 1846-579X
DOI: 10.7153/jmi-2021-15-36