Geodesic
On hop domination number of some generalized graph structures
Ural mathematical journal, Tome 7 (2021) no. 2, pp. 121-135 Cet article a éte moissonné depuis la source Math-Net.Ru

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A subset $ H \subseteq V (G) $ of a graph $G$ is a hop dominating set (HDS) if for every ${v\in (V\setminus H)}$ there is at least one vertex $u\in H$ such that $d(u,v)=2$. The minimum cardinality of a hop dominating set of $G$ is called the hop domination number of $G$ and is denoted by $\gamma_{h}(G)$. In this paper, we compute the hop domination number for triangular and quadrilateral snakes. Also, we analyse the hop domination number of graph families such as generalized thorn path, generalized ciliates graphs, glued path graphs and generalized theta graphs.
Keywords: hop domination number, snake graphs, theta graphs, generalized thorn path. 
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S. Shanmugavelan; C. Natarajan. On hop domination number of some generalized graph structures. Ural mathematical journal, Tome 7 (2021) no. 2, pp. 121-135. http://geodesic.mathdoc.fr/item/UMJ_2021_7_2_a8/

[1] Ayyaswamy S. K., Natarajan C., Hop Domination in Graphs, 2015 | MR

[2] Ayyaswamy S. K., Krishnakumari B., Natarajan C., Venkatakrishnan Y. B., “Bounds on the hop domination number of a tree”, Proc. Math. Sci., 125:4 (2015), 449–455 | DOI | MR | Zbl

[3] Balakrishnan R., Ranganathan K., A Textbook of Graph Theory, 2nd, Springer, NY, 2012, 292 pp. | DOI | MR | Zbl

[4] Durgun D. D., Lökçü B., “Weak and strong domination in thorn graphs”, Asian-Eur. J. Math., 13:4 (2020), 2050071 | DOI | MR | Zbl

[5] Gallian J. A., “A dynamic survey of graph Labeling”, Electron. J. Combin., 2021, DS6, 1–576 | DOI | MR

[6] Getchial Pon Packiavathi P., Balamurugan S., Gnanajothi R. B., “Hop domination number of caterpillar graphs”, Adv. Math. Sci. J., 9:5 (2020), 2739–2748 | DOI

[7] Gutman I., “Distance in thorny graph”, Publ. Inst. Math. (Beograd) (N.S.), 63:83 (1998), 31–36 http://eudml.org/doc/258067 | MR | Zbl

[8] Haynes T. W., Hedetniemi S. T., Henning M. A., Topics in Domination in Graphs, Springer, Cham, 2020, 545 pp. | DOI | MR | Zbl

[9] Haynes T. W., Hedetniemi S. T., Slater P. J., Fundamentals of Domination in Graphs, CRC Press, Boca Raton, 1998, 464 pp. | DOI | MR

[10] Haynes T. W., Hedetniemi S. T., Slater P. J., Domination in Graphs–Advanced Topics, CRC Press, Boca Raton, 1998, 520 pp. | DOI | MR

[11] Henning M. A., Rad N. J., “On 2-step and hop dominating sets in graphs”, Graphs Combin., 33 (2017), 913—927 | DOI | MR | Zbl

[12] Henning M. A., Pal S., Pradhan D., “Algorithm and hardness results on hop domination in graphs”, Inform. Process. Lett., 153 (2020), 1–8 | DOI | MR

[13] Natarajan C., Ayyaswamy S. K., “Hop domination in graphs-II”, An. St. Univ. Ovidius Constanta, 23:2 (2015), 187–199 | DOI | MR | Zbl

[14] Natarajan C., Ayyaswamy S. K., Sathiamoorthy G., “A note on hop domination number of some special families of graphs”, Int. J. Pure Appl. Math., 119:12f (2018), 14165–14171 https://www.acadpubl.eu/hub/2018-119-12/articles/6/1314.pdf

[15] Pabilona Y. M., Rara H. M., “Connected hop domination in graphs under some binary operations”, Asian-Eur. J. Math., 11:5 (2018), 1–11 | DOI | MR

[16] Rad N. J., Poureidi A., “On hop Roman domination in trees”, Comm. Combin. Optim., 4:2 (2019), 201–208 | DOI | MR | Zbl

[17] Rakim R. C., Saromines Ch. J. C., Rara H. M., “Perfect hop domination in graph”, Appl. Math. Sci., 12:13 (2018), 635–649 | DOI

[18] Salasalan G. P., Canoy S. R., Jr, “Global hop domination numbers of graphs”, Eur. J. Pure Appl. Math., 14:1 (2021), 112–125 | DOI | MR

[19] Sathiyamoorthy G., Janakiraman T. N., “Graceful labeling of generalized theta graphs”, Nat. Acad. Sci. Lett., 41:2 (2018), 121–122 | DOI | MR

[20] Shanmugavelan S., Natarajan C., “An updated survey on distance-based domination parameters in graphs”, Asia Math., 4:2 (2020), 134–149 http://www.asiamath.org/article/vol4iss2/AM-2008-4207.pdf