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Problems related to graph indices in trees

  • László SzékelyEmail author
  • Stephan Wagner
  • Hua Wang
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 159)

Abstract

In this chapter we explore recent development on various problems related to graph indices in trees. We focus on indices based on distances between vertices, vertex degrees, or on counting vertex or edge subsets of different kinds. Some of the indices arise naturally in applications, e.g., in chemistry, statistical physics, bioinformatics, and other fields, and connections are also made to other branches of graph theory, such as spectral graph theory. We will be particularly interested in the extremal values (maxima and minima) for different families of trees and the corresponding extremal trees. Moreover, we review results for random trees, consider localized versions of different graph indices and the associated notions of centrality, and finally discuss inverse problems, where one wants to find trees for which a specific graph index has a prescribed value.

Keywords

Wiener index Randic index Merrifield-Simmons index Hosoya index Random tree Inverse problems Dominating set Number of subtrees 

Mathematics Subject Classification (2000):

Primary: 05C05 Secondary 05C12 05C31 05C35 05C69 05C70 05C80 92E10 

Notes

Acknowledgements

This research was supported in part by the NSF DMS contract 1300547 and by the DARPA and AFOSR under the contract FA9550-12-1-0405 (László Székely), National Research Foundation of South Africa, grant number 96236 (Stephan Wagner), and Simons Foundation grant 245307 (Hua Wang).

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  2. 2.Department of Mathematical SciencesStellenbosch UniversityStellenboschSouth Africa
  3. 3.Department of Mathematical SciencesGeorgia Southern UniversityStatesboroUSA

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