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First degree-based entropy of graphs

  • A. Ghalavand
  • M. Eliasi
  • A. R. AshrafiEmail author
Original Research
  • 104 Downloads

Abstract

The first degree-based entropy of a connected graph G is defined as: \(I_1(G)=\log (\sum _{v_i\in V(G)}\deg (v_i))-\sum _{v_j\in V(G)}\frac{\deg (v_j)\log \deg (v_j)}{\sum _{v_i\in V(G)}\deg ( v_i)}\). In this paper, we apply majorization technique to extend some known results about the maximum and minimum values of the first degree-based entropy of trees, unicyclic and bicyclic graphs.

Keywords

Entropy Tree Degree sequence Unicyclic graph Bicyclic graph 

Notes

Acknowledgements

We are indebted to the referees for his/her suggestions and helpful remarks leaded us to improve this paper. The research of the third author is partially supported by the University of Kashan under Grant No. 572760/245.

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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.Department of Pure Mathematics, Faculty of Mathematical ScienceUniversity of KashanKashanIslamic Republic of Iran
  2. 2.Department of MathematicsKhansar Faculty of Mathematics and Computer ScienceKhansarIslamic Republic of Iran

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