Open Access
A Survey on the Randic Index
Xueliang Li,Yongtang Shi +1 more
TLDR
The general Randic index Rα(G) of a (chemical) graph G, defined as the sum of the weights (d(u)d(v))α of all edges uv of G, where d denotes the degree of a vertex u in G and α an arbitrary real number, was proposed by Milan Randic in 1975.Abstract:
The general Randic index Rα(G) of a (chemical) graph G, is defined as the sum of the weights (d(u)d(v))α of all edges uv of G, where d(u) denotes the degree of a vertex u in G and α an arbitrary real number, which is called the Randic index or connectivity index (or branching index) for α = −1/2 proposed by Milan Randic in 1975. The paper outlines the results known for the (general) Randic index of (chemical) graphs. Some very new results are released. We classify the results into the following categories: extremal values and extremal graphs of Randic index, general Randic index, zeroth-order general Randic index, higher-order Randic index. A few conjectures and open problems are mentioned.read more
Citations
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On a novel connectivity index
Bo Zhou,Nenad Trinajstić +1 more
TL;DR: In this paper, the sum-connectivity index for molecular graphs is proposed and several basic properties for this index, especially lower and upper bounds in terms of graph (structural) invariants.
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Chemical Graph Theory
Ernesto Estrada,Danail Bonchev +1 more
TL;DR: This chapter on chemical graph theory forms part of the natural science and processes section of the handbook.
Journal ArticleDOI
On Zagreb indices, Zagreb polynomials of some nanostar dendrimers
TL;DR: The hyper-Zagreb index, first multiple Zag Croatia index, second multiple ZAGreb index and Zagreb polynomials for some nanostar dendrimers are determined.
Journal ArticleDOI
Extremality of degree-based graph entropies
TL;DR: The main contribution of this paper is to prove some extremal values for the underlying graph entropy of certain families of graphs and to find the connection between the graph entropy and the sum of degree powers.
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On the normalized Laplacian energy and general Randić index R-1 of graphs
TL;DR: This paper considers the energy of a simple graph with respect to its normalized Laplacian eigenvalues, which is called the L-energy, and provides upper and lower bounds for L- energy based on its general Randic index R-1(G).
References
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Book
Graph theory with applications
TL;DR: In this paper, the authors present Graph Theory with Applications: Graph theory with applications, a collection of applications of graph theory in the field of Operational Research and Management. Journal of the Operational research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.
Book
Spectral Graph Theory
TL;DR: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigen values and quasi-randomness
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