NDLI: Independent Rainbow Domination Numbers of Generalized Petersen Graphs P(n,2) and P(n,3)

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Independent Rainbow Domination Numbers of Generalized Petersen Graphs P(n,2) and P(n,3)

Content Provider	MDPI
Author	Bo, štjan Gabrovšek Janez, Žerovnik Peperko, Aljoša
Copyright Year	2020
Description	We obtain new results on independent 2- and 3-rainbow domination numbers of generalized Petersen graphs $P(n,k)$ for certain values of $n,k\inN$ . By suitably adjusting and applying a well established technique of tropical algebra (path algebra) we obtain exact 2-independent rainbow domination numbers of generalized Petersen graphs $P(n,2)$ and $P(n,3)$ thus confirming a conjecture proposed by Shao et al. In addition, we compute exact 3-independent rainbow domination numbers of generalized Petersen graphs $P(n,2)$ . The method used here is developed for rainbow domination and for Petersen graphs. However, with some natural modifications, the method used can be applied to other domination type invariants, and to many other classes of graphs including grids and tori.
Starting Page	996
e-ISSN	22277390
DOI	10.3390/math8060996
Journal	Mathematics
Issue Number	6
Volume Number	8
Language	English
Publisher	MDPI
Publisher Date	2020-06-18
Access Restriction	Open
Subject Keyword	Mathematics Mathematical Physics Independent Rainbow Domination Independent Rainbow Domination Number Generalized Petersen Graphs Tropical Algebra Path Algebra
Content Type	Text
Resource Type	Article

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