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On a Relation Between

A conjecture of AutoGraphiX on the relation between the Randic index R and the algebraic connectivity a of a connected graph G is:

Extremality of degree-based graph entropies

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A Survey on the Randic Index

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…

Rainbow Connections of Graphs: A Survey

This survey attempts to bring together most of the results and papers that dealt with the concept of rainbow connection, including (strong) rainbow connection number, rainbow k-connectivity, k-rainbow index, rainbow vertex-connection number, algorithms and computational complexity.
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Fifty years of graph matching, network alignment and network comparison

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Graphs and Combinatorics

Graphs and Combinatorics is an international journal, which was established in 1985. It is devoted to research concerning all aspects of combinatorial mathematics, especially graph theory and…
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A Note on Distance-based Graph Entropies

This work explores graph entropies that are based on a novel information functional, which is the number of vertices with distance \(k\) to a given vertex, and investigates some properties thereof leading to a better understanding of this new information-theoretic quantity.
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Extremal Matching Energy of Bicyclic Graphs

The energy of a graph G is equal to the sum of the absolute values of the eigenvalues of G. Recently, Gutman and Wagner proposed the concept of the matching energy (ME) and pointed out that the…

Extremal Theta-free planar graphs

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The Turán number of star forests

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