On Average Hub Number of a Graph

Authors

DOI:

https://doi.org/10.26713/cma.v15i2.2664

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 the 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 of 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, URL: 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 Journal of Applied and Engineering Mathematics 12(1) (2022), 284 – 295, URL: https://jaem.isikun.edu.tr/web/images/articles/vol.12.no.1/25.pdf.

E. C. Cuaresma Jr. and R. N. Paluga, On the hub number of some graphs, Annals of Studies in Science and Humanities 1(1) (2015), 17 – 24, URL: https://core.ac.uk/download/231299682.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 integer lattice, Discrete Applied Mathematics 155(11) (2007), 1384 – 1394, DOI: 10.1016/j.dam.2007.02.007.

F. Harary, Graph Theory, Addison-Wesley Publishing Company, Reading, Massachusetts, ix + 274 pages (1969), URL: 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 domination number, Networks 58(3) (2011), 232 – 237, DOI: 10.1002/net.20433.

C.-H. Lin, J.-J. Liu, Y.-L. Wang, W. C.-K. Yen, The hub number of Sierpinski-like graphs, Theory of Computing Systems 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: 10.1016/j.ipl.2014.04.014.

J.-J. Liu, C. T.-H. Wang, Y.-L. Wang and W. C.-K. Yen, The hub number of co-comparability graphs, Theoretical Computer Science 570 (2015), 15 – 21, DOI: 10.1016/j.tcs.2014.12.011.

V. Mathad and S. Puneeth, Co-even hub number of a graph, Advances and Applications in Discrete Mathematics 39(2) (2023), 245 – 257, DOI: 10.17654/0974165823051.

V. Mathad, Anand and S. Puneeth, Bharath hub number of graphs, TWMS Journal of Applied and Engineering Mathematics 13(2) (2023), 661 – 669, URL: https://jaem.isikun.edu.tr/web/images/articles/vol.13.no.2/23.pdf.

R. E. Newman-Wolfe, R. D. Dutton and R. C. Brigham, Connecting sets in graphs – a domination related concept, Congressus Numerantium 67 (1988) 67 – 76.

M. Walsh, The hub number of a graph, International Journal of Mathematics and Computer Science 1 (2006), 117 – 124, URL: http://ijmcs.future-in-tech.net/R-Walsh.pdf.

Downloads

Published

14-11-2024
CITATION

How to Cite

Mathad, V., & Puneeth, S. (2024). On Average Hub Number of a Graph. Communications in Mathematics and Applications, 15(2), 753–763. https://doi.org/10.26713/cma.v15i2.2664

Issue

Section

Research Article