Sharp lower bounds for the Zagreb indices of unicyclic 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...
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By d(v|G) and d_2(v|G) are denoted the number of first and second neighborsof the vertex v of the graph G. The first, second, and third leap Zagreb indicesof G are defined asLM_1(G) = sum_{v in V(G)} d_2(v|G)^2, LM_2(G) = sum_{uv in E(G)} d_2(u|G) d_2(v|G),and LM_3(G) = sum_{v in V(G)} d(v|G) d_2(v|G), respectively. In this paper, we generalizethe results of Naji et al. [Commun. Combin. Optim. ...
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Recently, the first and second Zagreb indices are generalized into the variable Zagreb indices which are defined by M1(G) = ∑ u∈V (d(u))2λ and M2(G) = ∑ uv∈E (d(u)d(v)), where λ is any real number. In this paper, we prove that M1(G)/n M2(G)/m for all unicyclic graphs and all λ ∈ (−∞, 0]. And we also show that the relationship of numerical value between M1(G)/n and M2(G)/m is indefinite in the d...
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ژورنال
عنوان ژورنال: TURKISH JOURNAL OF MATHEMATICS
سال: 2015
ISSN: 1300-0098,1303-6149
DOI: 10.3906/mat-1205-44