Hub Number of Total Transformation Graphs

B. Basavanagoud; Mahammadsadiq Sayyed; Pooja B

doi:https://doi.org/10.14445/22315373/IJMTT-V68I7P511

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 7 | Year 2022 | Article Id. IJMTT-V68I7P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I7P511

Hub Number of Total Transformation Graphs

B. Basavanagoud, Mahammadsadiq Sayyed, Pooja B

Received	Revised	Accepted	Published
16 Jun 2022	25 Jul 2022	31 Jul 2022	05 Aug 2022

Abstract

For a graph 𝐺, the hub set 𝑆 is defined to be the subset of vertices of 𝐺 with the property that for any pair of vertices in 𝑉\𝑆, there exists a path with all intermediate vertices which belongs to 𝑆. The hub number of a graph 𝐺 is defined to be the smallest size of hub set. In this paper, we develop a method to find the hub number of total transformation graphs in terms of order and size of the graph considered.

Keywords

Hub set, Hub number, Total transformation graphs

References

[1] B. Basavanagoud, A. P. Barangi and I. N. Cangul, “Hub Number of Some Wheel Related Graphs,” Adv. Stud. Contem. Math. vol. 30, no. 3, pp. 325–334, 2020.
[2] B. Basavanagoud, M. Sayyed and A. P. Barangi, “Hub Number of Generalized Middle Graphs,” Twms J. App. Eng. Math. vol. 12, no. 1, pp. 284–295, 2022.
[3] W. Baoyindureng and M. Jixiang, “Basic Properties of Total Transformation Graphs,” J. Math. Study., vol. 34 no. 2 pp. 109 – 116, 2001.
[4] M. Behzad and G. Chartrand, “Total Graphs and Traversability,” Proc. Edinburgh. Math. Soc., vol. 15, pp. 117 – 120, 1966.
[5] E. C. Cuaresma Jr and R. N. Paluga, “On the Hub Number of Some Graphs,” Ann. Stud. Sci. Humanities, vol.1, no.1, pp. 17 – 24, 2015.
[6] J. A. Gallian, A Dynamic Survey of Graph Labeling, Electron J. Combin., vol.15, 2008.
[7] T. Grauman, S. G. Hartke, A. Jobson, B. Kinnersley, D. B. West, L. Wiglesworth, P. Worah, and H. Wu, “The Hub Number of a Graph,” Inform. Process. Lett., vol. 108, no. 4, pp. 226 – 228, 2008.
[8] F. Harary, Graph Theory, Addison-Wesley, Reading, 1969.
[9] P. Hamburger, R. Vandell and M. Walsh, “Routing Sets In the Integer Lattice,” Discrete Appl. Math. vol.155, pp.1384–1394, 2007.
[10] G. Indulal and A. Vijayakumar, “A Note on Energy of Some Graphs,” Match Commun. Math. Comput. Chem., vol.59, pp. 269 – 274, 2008.
[11] P. Johnson, P. Slater, M. Walsh, “the Connected Hub Number and the Connected Domination Number,” Networks, pp. 232–237, Doi 10.1002/Net.
[12] S. KlavzAr, U. Milutinović, “Graphs S(n, k) and A Variant of the Tower of Hanoi Problem,” Czechoslovak Math. J. vol.47, pp. 95– 104, 1997.
[13] X. Liu, Z. Dang, B. Wu, “the Hub Number, Girth and Mycielski Graphs,” Information Processing Letters, 2014, Http://Dx.Doi.Org/10.1016/J.Ipl.2014.04.014
[14] J. Liu, Cindy Tzu-Hsin Wang, Yue-Li Wang, William Chung-Kung Yen, “the Hub Number of Co-Comparability Graphs,” Theory Comput. Sci., vol. 570, pp.15–21, 2015.
[15] Veena Mathad, A. M. Sahal, and Kiran S., “The Total Hub Number of Graphs,” Bulletin Int. Math. Virtual Inst., vol.4, pp.61–67, 2014.
[16] H. Whitney, “Congruent Graphs and the Connectivity of Graphs,” Amer. J. Math., vol. 54, pp.150 – 168, 1932.
[17] M. Walsh, “the Hub Number of A Graph,” Int. J. Math. Comput. Sci., vol.1, no.1, pp.117 – 124, 2006.

Citation :

B. Basavanagoud, Mahammadsadiq Sayyed, Pooja B, "Hub Number of Total Transformation Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 7, pp. 75-83, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I7P511