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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.
Are motorways rational from slime mould’s point of view
 International Journal of Parallel, Emergent and Distributed Systems
, 2012
"... Abstract. We analyse the results of our experimental laboratory approximation of motorways networks with slime mould Physarum polycephalum. Motorway networks of fourteen geographical areas ..."
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Abstract. We analyse the results of our experimental laboratory approximation of motorways networks with slime mould Physarum polycephalum. Motorway networks of fourteen geographical areas
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.