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Connected Fair Domination in Graphs

  • Angsuman DasEmail author
  • Wyatt J. Desormeaux
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 655)

Abstract

In this paper, we introduce the notion of connected fair domination in graphs. A connected fair dominating set in a graph G (or \(\mathsf {CFD}\)-set) is a dominating set S such that \(\langle S \rangle \) is connected in G and all vertices not in S are dominated by the same number of vertices from S, i.e., every two vertices not in S has the same number of neighbours in S. The connected fair domination number of G (\(\mathsf {cfd}(G)\)) is the minimum cardinality of a \(\mathsf {CFD}\)-set in G. Apart from finding \(\mathsf {cfd}(G)\) for some standard graphs G, we proved various bounds on \(\mathsf {cfd}(G)\) in terms of order and some other graph parameters of G.

Keywords

Fair domination Connected domination Diagonal ramsey numbers 

Notes

Acknowledgement

The research is partially funded by NBHM Research Project Grant, (Sanction No. 2/48(10)/2013/ NBHM(R.P.)/R&D II/695), Government of India.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Department of MathematicsSt. Xavier’s CollegeKolkataIndia
  2. 2.Department of MathematicsUniversity of JohannesburgAuckland ParkSouth Africa

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