A note on Zagreb indices inequality for trees and unicyclic graphs
نویسندگان
چکیده
منابع مشابه
Leap Zagreb indices of trees and unicyclic graphs
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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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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Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree o...
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ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2011
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.173.9bb