On connected simple graphs and their degree sequences
Combinatorics
2015-12-19 v2
Abstract
This note describes necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a connected simple graph. Conditions are also given under which a sequence is necessarily connected i.e. the sequence can only be realised as a connected graph. A matrix is introduced whose non-empty entries partition the set of connected graphs. The note concludes with a result relating the number of edges in a simple graph to the connectedness of the graph.
Cite
@article{arxiv.1512.01377,
title = {On connected simple graphs and their degree sequences},
author = {Jonathan McLaughlin},
journal= {arXiv preprint arXiv:1512.01377},
year = {2015}
}
Comments
9 pages, 5 figures. arXiv admin note: text overlap with arXiv:1511.09321