An Efficient Algorithm to Test Forcibly-connectedness of Graphical Degree Sequences
We present an algorithm to test whether a given graphical degree sequence is forcibly connected or not and prove its correctness. We also outline the extensions of the algorithm to test whether a given graphical degree sequence is forcibly $k$-connected or not for every fixed $k\ge 2$. We show throu...
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doaj-71c1a824957040f0a53f86ad5705199f2020-11-25T00:09:36ZengGeorgia Southern UniversityTheory and Applications of Graphs2470-98592018-07-015210.20429/tag.2018.050202An Efficient Algorithm to Test Forcibly-connectedness of Graphical Degree SequencesKai WangWe present an algorithm to test whether a given graphical degree sequence is forcibly connected or not and prove its correctness. We also outline the extensions of the algorithm to test whether a given graphical degree sequence is forcibly $k$-connected or not for every fixed $k\ge 2$. We show through experimental evaluations that the algorithm is efficient on average, though its worst case run time is probably exponential. We also adapt Ruskey et al's classic algorithm to enumerate zero-free graphical degree sequences of length $n$ and Barnes and Savage's classic algorithm to enumerate graphical partitions of even integer $n$ by incorporating our testing algorithm into theirs and then obtain some enumerative results about forcibly connected graphical degree sequences of given length $n$ and forcibly connected graphical partitions of given even integer $n$. Based on these enumerative results we make some conjectures such as: when $n$ is large, (1) almost all zero-free graphical degree sequences of length $n$ are forcibly connected; (2) almost none of the graphical partitions of even $n$ are forcibly connected.https://digitalcommons.georgiasouthern.edu/tag/vol5/iss2/2graphical degree sequencegraphical partitionforcibly connectedforcibly $k$-connectedco-NP |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Kai Wang |
spellingShingle |
Kai Wang An Efficient Algorithm to Test Forcibly-connectedness of Graphical Degree Sequences Theory and Applications of Graphs graphical degree sequence graphical partition forcibly connected forcibly $k$-connected co-NP |
author_facet |
Kai Wang |
author_sort |
Kai Wang |
title |
An Efficient Algorithm to Test Forcibly-connectedness of Graphical Degree Sequences |
title_short |
An Efficient Algorithm to Test Forcibly-connectedness of Graphical Degree Sequences |
title_full |
An Efficient Algorithm to Test Forcibly-connectedness of Graphical Degree Sequences |
title_fullStr |
An Efficient Algorithm to Test Forcibly-connectedness of Graphical Degree Sequences |
title_full_unstemmed |
An Efficient Algorithm to Test Forcibly-connectedness of Graphical Degree Sequences |
title_sort |
efficient algorithm to test forcibly-connectedness of graphical degree sequences |
publisher |
Georgia Southern University |
series |
Theory and Applications of Graphs |
issn |
2470-9859 |
publishDate |
2018-07-01 |
description |
We present an algorithm to test whether a given graphical degree sequence is forcibly connected or not and prove its correctness. We also outline the extensions of the algorithm to test whether a given graphical degree sequence is forcibly $k$-connected or not for every fixed $k\ge 2$. We show through experimental evaluations that the algorithm is efficient on average, though its worst case run time is probably exponential. We also adapt Ruskey et al's classic algorithm to enumerate zero-free graphical degree sequences of length $n$ and Barnes and Savage's classic algorithm to enumerate graphical partitions of even integer $n$ by incorporating our testing algorithm into theirs and then obtain some enumerative results about forcibly connected graphical degree sequences of given length $n$ and forcibly connected graphical partitions of given even integer $n$. Based on these enumerative results we make some conjectures such as: when $n$ is large, (1) almost all zero-free graphical degree sequences of length $n$ are forcibly connected; (2) almost none of the graphical partitions of even $n$ are forcibly connected. |
topic |
graphical degree sequence graphical partition forcibly connected forcibly $k$-connected co-NP |
url |
https://digitalcommons.georgiasouthern.edu/tag/vol5/iss2/2 |
work_keys_str_mv |
AT kaiwang anefficientalgorithmtotestforciblyconnectednessofgraphicaldegreesequences AT kaiwang efficientalgorithmtotestforciblyconnectednessofgraphicaldegreesequences |
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1725411039334367232 |