Extremal Graph Theory for Degree Sequences
Combinatorics
2015-10-08 v1
Abstract
This paper surveys some recent results and progress on the extremal prob- lems in a given set consisting of all simple connected graphs with the same graphic degree sequence. In particular, we study and characterize the extremal graphs having the maximum (or minimum) values of graph invariants such as (Laplacian, p-Laplacian, signless Laplacian) spectral radius, the first Dirichlet eigenvalue, the Wiener index, the Harary index, the number of subtrees and the chromatic number etc, in given sets with the same tree, unicyclic, graphic degree sequences. Moreover, some conjectures are included.
Cite
@article{arxiv.1510.01903,
title = {Extremal Graph Theory for Degree Sequences},
author = {Xiao-Dong Zhang},
journal= {arXiv preprint arXiv:1510.01903},
year = {2015}
}
Comments
22 pages, 2 figures. arXiv admin note: text overlap with arXiv:1209.2188 by other authors