Asian Research Journal of Mathematics

  • About
    • About the Journal
    • Submissions & Author Guideline
    • Accepted Papers
    • Editorial Policy
    • Editorial Board Members
    • Reviewers
    • Propose a Special Issue
    • Reprints
    • Subscription
    • Membership
    • Publication Ethics and Malpractice Statement
    • Digital Archiving Policy
    • Contact
  • Archives
  • Indexing
  • Publication Charge
  • Submission
  • Testimonials
  • Announcements
Advanced Search
  1. Home
  2. Archives
  3. 2022 - Volume 18 [Issue 8]
  4. Original Research Article

Submit Manuscript


Subscription



  • Home Page
  • Author Guidelines
  • Editorial Board Member
  • Editorial Policy
  • Propose a Special Issue
  • Membership

On the Restrained Cost Eective Sets of Some Special Classes of Graphs

  • Darwin P. Mangubat
  • Isagani S. Cabahug, Jr.

Asian Research Journal of Mathematics, Page 22-34
DOI: 10.9734/arjom/2022/v18i830395
Published: 22 June 2022

  • View Article
  • Download
  • Cite
  • References
  • Statistics
  • Share

Abstract


Let G be a nontrivial, undirected, simple graph. Let S be a subset of V (G). S is a restrained cost effective set of G if for each vertex v in S, degS(v) \(\leq\) degV (G)rS(v) and the subgraph induced by the vertex set, V (G) r S has no isolated vertex. The maximum cardinality of a restrained cost effective set is the restrained cost effective number, CEr(G). In this paper, the restrained cost effective sets of paths, cycles, complete graphs, complete product of graphs and graphs resulting from line graph of graphs with maximum degree of 2 were characterized. As a direct consequence, the bounds or exact values for the restrained cost effective number were determined as well.


Keywords:
  • Restrained cost effective set
  • restrained cost effective number
  • line graph
  • Full Article – PDF
  • Review History

How to Cite

Mangubat, D. P., & Jr., I. S. C. (2022). On the Restrained Cost Eective Sets of Some Special Classes of Graphs. Asian Research Journal of Mathematics, 18(8), 22-34. https://doi.org/10.9734/arjom/2022/v18i830395
  • ACM
  • ACS
  • APA
  • ABNT
  • Chicago
  • Harvard
  • IEEE
  • MLA
  • Turabian
  • Vancouver

References

Hedetniemi SM, Hedetniemi ST, Kennedy K, McRae A. Self-stabilizing algorithms for

unfriendly partitions into two disjoint dominating sets. Parallel Process. Lett. 2003;23(1):11.

Haynes C, Hedetniemi S. Client-server and cost eective sets in graphs. AKCE International

Journal of Graphs and Combinatorics. 2018;15(2):211-218.

Caadan JG, Paluga RN, Aniversario IS. Upper distance k-cost eective number in the join of

graphs. European Journal of Pure and Applied Mathematics. 2020;13(3):701-709.

McCoy T. Cost eective domination in graphs. Electronic Theses and Dissertations. 2012;Paper

Domke G, Hattingh J, Hedetniemi S, Laskar R, Markus L. Restrained Domination in Graphs.

Discrete Mathematics. 1999;203(1-3):61-69.

Acosta HR, Eballe RG, Cabahug IS. Downhill domination in the tensor product of graphs.

International Journal of Mathematical Analysis. 2018;13(12):555-564.

Cabahug IS, Canoy SR. Connected dr-Power Dominating Sets in Graphs. Advances and

Applications in Discrete Mathematics. 2018;19(3):171-182.

Harary F. Graph Theory. United States of America: Addison- Wesley Publishing Company,

Inc; 1969.

Kratica J. Computing strong metric dimension of some special classes of graphs by genetic

algorithms. Yugoslav Journal of Operations Research. 2016;18(2).

Meena S, Vaithilingam K. Prime Labeling For Some Fan Related Graphs. International Journal

of Engineering Research and Technology. 2012;1(9):2-3.

More R, Archana S, Dandwate D, Tupe U. A Literature Review on Applications of Graph

Theory in Various Fields. International Journal for Research Trends and Innovation (IJRTI).

;6(1):1-8.

Chartrand G, Lesniak L, Zhang P. Introduction to Graph Theory. Chapman and Hall/CRC;

Cabahug IS, Canoy SR. Independent dr-power dominating sets in graphs. Applied

Mathematical Sciences. 2016;10(8):377-387.

Cabahug IS, Canoy SR. dr-Power dominating sets in graphs. International Journal of

Mathematical Analysis. 2016;10(3):139-149.

Demange M, Monnot J, Pop P, Ries B. On the complexity of the selective graph coloring

problem in some special classes of graphs. Theoretical Computer Science. 2014;540:89-102.
  • Abstract View: 66 times
    PDF Download: 29 times

Download Statistics

Downloads

Download data is not yet available.
  • Linkedin
  • Twitter
  • Facebook
  • WhatsApp
  • Telegram
Make a Submission / Login
Information
  • For Readers
  • For Authors
  • For Librarians
Current Issue
  • Atom logo
  • RSS2 logo
  • RSS1 logo


© Copyright 2010-Till Date, Asian Research Journal of Mathematics. All rights reserved.