# Graphs with minimum degree-based entropy

@article{Dong2021GraphsWM, title={Graphs with minimum degree-based entropy}, author={Yanni Dong and Maximilien Gadouleau and Pengfei Wan and Shenggui Zhang}, journal={ArXiv}, year={2021}, volume={abs/2108.13884} }

The degree-based entropy of a graph is defined as the Shannon entropy based on the information functional that associates the vertices of the graph with the corresponding degrees. In this paper, we study extremal problems of finding the graphs attaining the minimum degree-based graph entropy among graphs and bipartite graphs with a given number of vertices and edges. We characterize the unique extremal graph achieving the minimum value among graphs with a given number of vertices and edges and…

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## References

SHOWING 1-10 OF 19 REFERENCES

Extremality of degree-based graph entropies

- Mathematics, Computer ScienceInf. Sci.
- 2014

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.

Graph entropy based on the number of spanning forests of c-cyclic graphs

- Computer Science, MathematicsAppl. Math. Comput.
- 2019

A new graph entropy measure that is based on the number of spanning forests is developed and it is shown that the cycle graph Cn attains the maximal value of the entropy for unicyclic graphs with order n and large cycle lengths.

On the extremal values of general degree-based graph entropies

- Mathematics, Computer ScienceInf. Sci.
- 2016

This note proves one part of the conjecture about upper and lower bounds of the degree-based graph entropy Ik(T) in the class of trees introduced in S. Cao, M. Dehmer, and Y. Shi (2014) using Lagrange multipliers and Jensen's inequality, and disprove the other part by providing a family of counter-examples.

On graph entropy measures based on the number of independent sets and matchings

- Computer Science, MathematicsInf. Sci.
- 2020

Some upper and lower bounds as well as some information inequalities for these information-theoretic quantities for graph entropy measures are established and results reveal the two entropies possess some new features.

Network Entropies Based on Independent Sets and Matchings

- Mathematics, Computer ScienceAppl. Math. Comput.
- 2017

Entropy-based measures have been used to characterize the structure of complex networks. Various graph entropies based on different graph parameters have been proposed and studied. So, it has been…

First degree-based entropy of graphs

- Mathematics
- 2019

The first degree-based entropy of a connected graph G is defined as: $$I_1(G)=\log (\sum _{v_i\in V(G)}\deg (v_i))-\sum _{v_j\in V(G)}\frac{\deg (v_j)\log \deg (v_j)}{\sum _{v_i\in V(G)}\deg (…

A history of graph entropy measures

- Computer Science, MathematicsInf. Sci.
- 2011

Methods for measuring the entropy of graphs are described and relationships between selected entropy measures are examined, illustrating differences quantitatively with concrete examples.

Difference graphs

- Computer ScienceDiscret. Math.
- 2004

It is shown that for every graph G there exists a large enough k such that G arises with any of the definitions above, and it is proved that with the first two definitions one may need k = Ω(log n) in any such realizations of certain graphs on n vertices.

Threshold graphs and related topics

- Mathematics
- 1995

Preface. Basic Terminology. Threshold Graphs. Motivation. Basic characterizations. Minimizing integral weights. Perfect graphs and algorithms. Threshold and split completions. Longest cycles and…

Degree Powers in Graphs: The Erdős–Stone Theorem

- Computer Science, MathematicsCombinatorics, Probability and Computing
- 2012

This statement is used to strengthen the Erdős–Stone theorem by using ∑v ∈ V(G)dp(v) instead of the number of edges.