On Accurate Domination in Graphs

Open access

Abstract

A dominating set of a graph G is a subset DVG such that every vertex not in D is adjacent to at least one vertex in D. The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. The accurate domination number of G, denoted by γa(G), is the cardinality of a smallest set D that is a dominating set of G and no |D|-element subset of VG \ D is a dominating set of G. We study graphs for which the accurate domination number is equal to the domination number. In particular, all trees G for which γa(G) = γ(G) are characterized. Furthermore, we compare the accurate domination number with the domination number of different coronas of a graph.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] G. Chartrand L. Lesniak and P. Zhang Graphs and Digraphs (CRC Press Boca Raton 2016).

  • [2] M. Dettlaff M. Lemańska J. Topp and P. Żyliński Coronas and domination subdivision number of a graph Bull. Malays. Math. Sci. Soc. 41 (2018) 1717–1724. doi:10.1007/s40840-016-0417-0

  • [3] K. Dhanalakshmi and B. Maheswari Accurate and total accurate dominating sets of interval graphs Int. J. Comput. Eng. Tech. 5 (2014) 85–93.

  • [4] M. Fischermann Block graphs with unique minimum dominating sets Discrete Math. 240 (2001) 247–251. doi:10.1016/S0012-365X(01)00196-0

  • [5] R. Frucht and F. Harary On the corona of two graphs Aequationes Math. 4 (1970) 322–324. doi:10.1007/BF01844162

  • [6] V.M. Goudar S.H. Venkatesh Venkatesha and K.M. Tejaswini Accurate connected edge domination number in graphs J. Ultra Sci. Phys. Sci. Ser. A 29 (2017) 290–301. doi:10.22147/jusps-A/290708

  • [7] V.M. Goudar S.H. Venkatesh Venkatesha and K.M. Tejaswini Total accurate edge domination number in graphs Int. J. Math. Sci. Eng. Appl. 11 (2017) 9–18.

  • [8] G. Gunther B. Hartnell L.R. Markus and D. Rall Graphs with unique minimum dominating sets Congr. Numer. 101 (1994) 55–63.

  • [9] T.W. Haynes S.T. Hedetniemi and P.J. Slater Fundamentals of Domination in Graphs (Marcel Dekker Inc. New York 1998).

  • [10] I. Kelkar and B. Maheswari Accurate domination number of butterfly graphs Chamchuri J. Math. 1 (2009) 35–43.

  • [11] V.R. Kulli and M.B. Kattimani The accurate domination number of a graph Technical Report 2000:01 (Dept. Math. Gulbarga University Gulbarga 2000).

  • [12] V.R. Kulli and M.B. Kattimani Accurate domination in graphs in: Advances in Domination Theory I V.R. Kulli (Ed.) (Vishwa International Publications 2012) 1–8.

  • [13] V.R. Kulli and M.B. Kattimani Global accurate domination in graphs Int. J. Sci. Res. Pub. 3 (2013) 1–3.

  • [14] V.R. Kulli and M.B. Kattimani Connected accurate domination in graphs J. Comput. Math. Sci. 6 (2015) 682–687.

  • [15] C.M. Mynhardt Vertices contained in every minimum dominating set of a tree J. Graph Theory 31 (1999) 163–177. doi:10.1002/(SICI)1097-0118(199907)31:3h163::AID-JGT2i3.0.CO;2-T

  • [16] S.H. Venkatesh V.M. Goudar and Venkatesha Operations on accurate edge domination number in graphs Glob. J. Pure Appl. Math. 13 (2017) 5611–5623.

  • [17] S.H. Venkatesh V.R. Kulli V.M. Goudar and Venkatesha Results on accurate edge domination number in graphs J. Ultra Sci. Phys. Sci. Ser. A 29 (2017) 21–29. doi:10.22147/jusps-A/290104

Search
Journal information
Impact Factor

IMPACT FACTOR 2018: 0.741
5-year IMPACT FACTOR: 0.611

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.763
Source Normalized Impact per Paper (SNIP) 2018: 0.934

Mathematical Citation Quotient (MCQ) 2018: 0.42

Target audience:

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs

Metrics
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 170 170 23
PDF Downloads 93 93 8