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The structure of graphs with no cycl...

ProQuest Information and Learning Co.

The structure of graphs with no cycles of length 0 (mod 3).

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	The structure of graphs with no cycles of length 0 (mod 3)./
Author:	Gauthier, Gregory.
Description:	1 online resource (87 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
Contained By:	Dissertation Abstracts International78-11B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355041439

The structure of graphs with no cycles of length 0 (mod 3).
Gauthier, Gregory.

The structure of graphs with no cycles of length 0 (mod 3). - 1 online resource (87 pages)

Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

We examine the structure of graphs that have no cycles of length 0 (mod 3). We show that, if G is a simple 2-connected graph with no cycles of length 0 (mod 3), then G has two adjacent degree two vertices or G has two nonadjacent degree two vertices with the same neighborhood. Using this result, it follows that if G is a simple graph with no cycles of length 0 (mod 3), then for every induced subgraph H of G, the modularity of H, defined as the number of even independent sets minus the number of odd independent sets, is either --1, 0, or 1.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355041439Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

The structure of graphs with no cycles of length 0 (mod 3).
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020 $a 9780355041439
035 $a (MiAaPQ)AAI10284031
035 $a (MiAaPQ)princeton:12161
035 $a AAI10284031
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Gauthier, Gregory. $3 1180763
245 1 4 $a The structure of graphs with no cycles of length 0 (mod 3).
264 0 $c 2017
300 $a 1 online resource (87 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
500 $a Adviser: Paul D. Seymour.
502 $a Thesis (Ph.D.) $c Princeton University $d 2017.
504 $a Includes bibliographical references
520 $a We examine the structure of graphs that have no cycles of length 0 (mod 3). We show that, if G is a simple 2-connected graph with no cycles of length 0 (mod 3), then G has two adjacent degree two vertices or G has two nonadjacent degree two vertices with the same neighborhood. Using this result, it follows that if G is a simple graph with no cycles of length 0 (mod 3), then for every induced subgraph H of G, the modularity of H, defined as the number of even independent sets minus the number of odd independent sets, is either --1, 0, or 1.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Princeton University. $b Mathematics. $3 1180706
773 0 $t Dissertation Abstracts International $g 78-11B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10284031 $z click for full text (PQDT)

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