Problems Related to Graph Indices in Trees
Document Type
Contribution to Book
Publication Date
2016
Publication Title
Recent Trends in Combinatorics
DOI
10.1007/978-3-319-24298-9_1
ISSN
2198-3224
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.
Recommended Citation
Szekely, Laszlo A., Stephen Wagner, Hua Wang.
2016.
"Problems Related to Graph Indices in Trees."
Recent Trends in Combinatorics, Andrew Beveridge, Jerrold R. Griggs, Leslie Hogben, Gregg Musiker, and Prasad Tetali (Ed.): 3-30 Cham, Switzerland: Springer International Publishing.
doi: 10.1007/978-3-319-24298-9_1
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/711
