The Maximum Number of Dominating Induced Matchings

A matching M of a graph G is a dominating induced matching (DIM) of G if every edge of G is either in M or adjacent with exactly one edge in M. We prove sharp upper bounds on the number μ(G) of DIMs of a graph G and characterize all extremal graphs. Our results imply that if G is a graph of order n,...

Full description

Saved in:
Bibliographic Details
Published inJournal of graph theory Vol. 78; no. 4; pp. 258 - 268
Main Authors Lin, Min Chih, Moyano, Veronica A., Rautenbach, Dieter, Szwarcfiter, Jayme L.
Format Journal Article
LanguageEnglish
Published Hoboken Blackwell Publishing Ltd 01.04.2015
Wiley Subscription Services, Inc
Subjects
dominating induced matching
Fibonacci numbersAMS subject classification: 05c35
Online AccessGet full text

Cover

More Information
Summary:A matching M of a graph G is a dominating induced matching (DIM) of G if every edge of G is either in M or adjacent with exactly one edge in M. We prove sharp upper bounds on the number μ(G) of DIMs of a graph G and characterize all extremal graphs. Our results imply that if G is a graph of order n, then μ(G)≤3n3; μ(G)≤4n5 provided G is triangle‐free; and μ(G)≤4n−15 provided n≥9 and G is connected.
Bibliography:PICT ANPCyT - No. 1970
CNPq
FAPERJ
PIP CONICET - No. 11220100100310
ark:/67375/WNG-WBF04XSJ-2
ArticleID:JGT21804
CAPES
istex:4D6D092DEA3E29026DD71C6268D04A8D4C508971
UBACyT - No. 20020100100754; No. 20020090100149
CAPES/DAAD Probral Project Cycles, Convexity, and Searching
Contract grant sponsor: UBACyT; contract grant numbers: 20020100100754 and 20020090100149 (to M.C.L. and V.A.M.); contract grant sponsor: PICT ANPCyT; contract grant number: 1970 (to M.C.L. and V.A.M.); contract grant sponsor: PIP CONICET; contract grant number: 11220100100310 (to M.C.L. and V.A.M.); contract grant sponsor: CAPES/DAAD Probral Project Cycles, Convexity, and Searching in Graphs (to D.R.); contract grant sponsor: CNPq (to J.L.S.); contract grant sponsor: CAPES (to J.L.S.); contract grant sponsor: FAPERJ (to J.L.S.).
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.21804