On Average Hub Number of a Graph

Authors

Keywords:

Hub set, average hub number

Abstract

The idea of local and average hub numbers is explored as an expansion of the hub number in graphs, a connectivity measure that holds significance in transportation networks. In this analysis, we investigate the characterization of graphs by examining their local and average hub numbers and study them for graph classes namely trees and thorn graphs. Additionally, we determine the precise values of the average hub number for certain graph operations and discuss the bounds using Nordhaus-Gaddum type inequalities.

Downloads

Download data is not yet available.

References

E. Aslan and A. Kirlangic, The Average Lower Domination Number of Graphs, Bulletin

of the International Mathematical Virtual Institute 3 (2013), 155 { 160, http://elib.mi.

sanu.ac.rs/files/journals/bimvi/5/bimvin5p155-60.pdf.

B. Basavanagoud, M. Sayyed and A. P. Barangi, Hub Number of Generalized Middle

Graphs, TWMS J. App. and Eng. Math. 12(1) (2022), 284 { 295, https://jaem.isikun.

edu.tr/web/images/articles/vol.12.no.1/25.pdf.

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, Information Processing Letters 108(4)

(2008), 226 { 228, doi:10.1016/j.ipl.2008.05.022.

P. Hamburger, R. Vandell, and M. Walsh, Routing Sets in the Inte-

ger Lattice, Discrete Applied Mathematics 155(11) (2007), 1384 { 1394,

doi:https://doi.org/10.1016/j.dam.2007.02.007.

F. Harary, Graph Theory, Addison Wesley Publishing Company, Reading Massachusetts

(1969), https://users.metu.edu.tr/aldoks/341/Book%201%20(Harary).pdf.

P. Johnson, P. Slater, and M.Walsh, The Connected Hub Number and the Connected Dom-

ination Number, Networks 58(3) (2011), 232 { 237, doi:https://doi.org/10.1002/net.20433.

S. I. Khalaf V. Mathad and S. S. Mahde, Hub and Global Hub Numbers of a

Graph, Proceedings of the Jangjeon Mathematical Society 23(2) (2020), 231 { 239,

doi:10.17777/pjms2020.23.2.231.

C.H. Lin, J.J. Liu, Y.L. Wang, W.C.K. Yen, The Hub Number of Sierpinski-Like Graphs,

Theory Comput. Syst. 49(3) (2011), 588 { 600, doi:10.1007/s00224-010-9286-3.

X. Liu, Z. Dang, and B. Wu, The Hub Number, Girth and Mycielski Graphs, Information

Processing Letters 114(10) (2014), 561 { 563, doi:https://doi.org/10.1016/j.ipl.2014.04.014.

J. J. Liu, C. T.H. Wang, Y.L. Wang, W. C.K. Yen, The Hub Number of

Co-comparability Graphs, Theoretical Computer Science 570 (2015), 15 { 21,

doi:https://doi.org/10.1016/j.tcs.2014.12.011.

V. Mathad, Anand and Puneeth S., Bharath Hub Number of Graphs, TWMS J. App.

and Eng. Math. 13(2) (2023), 661 { 669, https://jaem.isikun.edu.tr/web/images/

articles/vol.13.no.2/23.pdf.

V. Mathad and Puneeth S., Co-even Hub Number of a Graph, Ad-

vances and Applications in Discrete Mathematics 39(2) (2023), 245 { 257,

doi:http://dx.doi.org/10.17654/0974165823051.

V. Mathad, A. M. Sahal, and Kiran S, The Total Hub Number of Graphs,

Bulletin of the International Mathematical Virtual Institute 4 (2014), 61 { 67,

doi:10.13140/RG.2.2.25636.50568.

R.E. Newman-Wolfe, R.D. Dutton, R.C. Brigham, Connecting sets in graphs

a domination related concept, Congr. Numer. 67 (1988) 67 { 76, https:

//www.researchgate.net/publication/267184069_Connecting_sets_in_graphs_

-_a_domination_related_concept.

M. Walsh, The Hub Number of a Graph, International Journal of Mathematics and Com-

puter Science 1 (2006), 117 { 124, http://ijmcs.future-in-tech.net/R-Walsh.pdf.

Published

14-11-2024

How to Cite

Puneeth, S., & Mathad, V. (2024). On Average Hub Number of a Graph. Communications in Mathematics and Applications, 15(2). Retrieved from https://rgnpublications.com/journals/index.php/cma/article/view/2664

Issue

Vol. 15 No. 2 (2024)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.