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On the Randic ́ index of cacti
"... The Randic ́ index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))− 1 2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. In the paper, we give a sharp lower bound on the Randić index of cacti. ..."
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The Randic ́ index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))− 1 2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. In the paper, we give a sharp lower bound on the Randić index of cacti.
On the Randić index of quasitree graphs
 J. Math. Chem
"... The Randic ́ index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))−1/2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertex u and v in G. A graph G is called quasitree, if there exists u ∈ V (G) such that G −u is a tree. In the paper, we giv ..."
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The Randic ́ index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))−1/2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertex u and v in G. A graph G is called quasitree, if there exists u ∈ V (G) such that G −u is a tree. In the paper, we give sharp lower and upper bounds on the Randić index of quasitree graphs. KEY WORDS: Randic ́ index, quasitree graph, cycle 1.
On a variation of Randić index
, 2011
"... Randić index, R, also known as the connectivity or branching index, is an important topological index in chemistry. In order to attack some conjectures concerning Randić index, Dvoˇrák et al. [5] introduced a modification of this index, denoted by R ′. In this paper we present some of the basic prop ..."
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Randić index, R, also known as the connectivity or branching index, is an important topological index in chemistry. In order to attack some conjectures concerning Randić index, Dvoˇrák et al. [5] introduced a modification of this index, denoted by R ′. In this paper we present some of the basic properties of R ′. We determine graphs with minimal and maximal values of R ′ , as well as graphs with minimal and maximal values of R ′ among the trees and unicyclic graphs. We also show that if G is a trianglefree graph on n vertices with minimum degree δ, then R ′ (G) ≥ δ. Moreover, equality holds only for the complete bipartite graph Kδ,n−δ.
Some Distance and Degree Graph INVARIANTS AND FULLERENE STRUCTURES
, 2013
"... In the thesis we concentrate to the part of graph theory that can be applied in chemistry. One of the aims is applying graphtheoretical methods to predict the properties of a chemical compound based on its molecule structure. Molecular descriptors or topological indices is one way of predicting so ..."
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In the thesis we concentrate to the part of graph theory that can be applied in chemistry. One of the aims is applying graphtheoretical methods to predict the properties of a chemical compound based on its molecule structure. Molecular descriptors or topological indices is one way of predicting some properties. We dedicate our attention to Zagreb indices, a modification of Randic ́ index called R ′ index, and Gutman index. For a simple graphG with n vertices andm edges, the inequalityM1(G)/n ≤M2(G)/m, where M1(G) and M2(G) are the first and the second Zagreb indices of G, is known as Zagreb indices inequality. We characterize the intervals of vertex degrees that satisfy this inequality, and find an infinite family of connected graphs dissatisfying this inequality. We also present an algorithm that decides if an arbitrary set of vertex degrees satisfies the inequality and consider variable Zagreb index inequality. We also determine the graphs with extremal values for Gutman and R ′ indices, and find a trianglefree graph on n vertices with minimum R′(G) index. Fullerene molecules are carbon cage molecules arranged only in pentagons and hexagons.