Radius, diameter, domination number, order and minimum degree
*P. MafutaCorresponding authorphillipmafuta@gmail.comDepartment of Mathematics and Applied Mathematics IB74University of the Free StateBloemfontein, P. O. Box 339, 9300, South AfricaView full profile →
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- Received:
- 12 Oct 2022
- Published Online:
- 12 Aug 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1398
- Pages:
- 1281–1291
Abstract
Keywords
Subject Classifications
References
[1] Ananchuen N., Ananchuen W., Plummer M.D., Domination in Graphs, In: Dehmer M. (eds) Structural Analysis of Complex Networks. Birkhuser Boston (2011), https://doi.org/10.1007/978-0-8176-4789-64.
[2] Alfuraidan M.R., Das K.C., Vetr k T., Balachandran S., General sum-connectivity index of unicyclic graphs with given diameter, Discrete Applied Mathematics, 295, 39-46 (2021).
[3] Caro Y., West D.B., Yuster R., Connected domination and spanning trees with many leaves, SIAM Journal on Discrete Mathematics 13, 202-211 (2000).
[4] Chung F.K.R., The average distance and the independence number, Journal of Graph Theory, 12, 229-235 (1988).
[5] Dankelmann P., Dlamini G., and Swart H.C., Upper bounds on the distance measures in -free graphs, Utilitas Mathenatica, 67, 205-222 (2005).
[6] Dankelmann P., Entringer R.C., Average distance, minimum degree and spanning trees, Journal of Graph Theory, 33, 1-13 (2000).
[7] Dankelmann P., and Mukwembi S., The Distance Concept and Distance in Graphs, In I Gutman, B. Furtula (Eds), Distance in Molecular Graphs-Theory, Univ. Kragujevac, Kragujevac, 3-48 (2012).
[8] Dankelmann P., Swart H.C., and van den Berg P., Diameter and inverse degree, Discrete Mathematics, 308, 670-673 (2008).
[9] DeLaviña E., Pepper B., and Waller B., Lower bounds for the domination number, Discussiones Mathematicae: Graph Theory, 30(3), 475-487 (2010).
[10] Das A. Triameter of Graphs, Discussiones Mathematicae: Graph Theory, 41(2), 601-616 (2021).
[11] Desormeaux W.J., Haynes T.W., and Henning M.A., Restrained domination in self-complementary graphs. Discussiones Mathematicae: Graph Theory, 41(2), 633-645 (2021).
[12] Erdös P., Pach J., and Spencer J., On the mean distance between points of a graph, Congressus Numerantium, 64, 121-124 (1988).
[13] Erdös P., Pach J., Pollack R. and Tuza Z., Radius, diameter and minimum degree, Journal of Combinatorial Theory, Series B, 47, 73-79 (1989).
[14] Erdös P., Sachs M. and Sos V., Maximum induced trees in graphs, Journal of Combinatorial Theory, Series B, 41, 61-79 (1986).
[15] Griggs J.R., Wu M., Spanning trees in graphs of minimum degree 4 or 5. Discrete Mathematics, 104, 167-183 (1992).
[16] Haynes T.W., Hedetniemi S.M., Hedetniemi S.T., Henning M.A., Domination in Graphs, Advanced Topics, Marcel Dekker, New York, (1998).
[17] Haynes T.W., Hedetniemi S.M., Hedetniemi S.T., and Henning M.A., Domination in graphs applied to electric power networks, Siam Journal on Discrete Mathematics, 15(4), 519-529 (2002).
[18] Henning M.A., Mukwembi S., Domination, radius and minimum Degree, Discrete Applied Mathematics, 157, 2964-2968 (2009).
[19] Liu, C. A note on domination number in maximal outerplanar graphs, Discrete Applied Mathematics, 293, 90-94 (2021).
[20] Mafuta P., On the leaf number of a graph, DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences-Seminar Series, (2021). https://youtu.be/Ih6pOB6X9ro.
[21] Mafuta P. Bounds on the leaf number in graphs of girth 4 or 5, Journal of Discrete Mathematical Sciences and Cryptography, 24(6), 1573-1582 (2021).
[22] Mafuta P., Mukwembi S., & Munyira S., Radius, leaf number, connected domination number and minimum degree, Quaestiones Mathematicae, 46(5), 1009-1016 (2023).
[23] Mafuta P., Mukwembi S., Rodrigues B.G., A note on connected domination number and leaf number. Discrete Mathematics 346(2), 113228 (2023).
[24] Mahadevan G., Vijayalakshmi V., Clone hop domination number of a graph, Journal of Discrete Mathematical Sciences and Cryptography, 22(5), 719-729 (2019).
[25] Mukwembi S., On size, order, diameter and minimum degree, Indian Journal of Pure and Applied Mathamatics, 44(4), 467-472 (2013).
[26] Mukwembi S., On size, radius and minimum degree, Discrete Mathematics and Theoretical Computer Science, 16(1), 1-6 (2014).
[27] Munyira S., Bounds on distance-based parameters, University of Zimbabwe, 1-108 (2016).
[28] Natarajan C., Ayyaswamy S., Hop domination in graphs II, Versita, 23(2), 187-199 (2015).
[29] Raju M., Bhutani K.R., Moazzez B., Arumugam S., On F-domination in graphs, AKCE International Journal of Graphs and Combinatorics. https://doi.org/10.1016/j.akcej.2018.07.004.
[30] Wu B., Ani X., Liu G., Yan G. and Liu X., Minimum degree, edge-connectivity and radius, Journal of Combinatorial Optimization, 26, 585-591 (2013).
[31] Yan H., Kang L. and Xu G., The exact domination number of the generalized Petersen graphs. Discrete Mathematics, 309(8), 2596-2607 (2009).




