CFP last date
20 May 2024
Call for Paper
June Edition
IJCA solicits high quality original research papers for the upcoming June edition of the journal. The last date of research paper submission is 20 May 2024

Submit your paper
Know more
The week's pick
Responsive image
Enhancing Privacy Preservation: Multi-Attribute Protection with P-Sensitive K-Anonymity

Twinkle Patel Kiran Amin
Random Articles
Reseach Article

Hop Hubtic Number and Hop Hub Polynomial of Graphs

by Abdu-Alkafi Saead Sand, Sultan Senan Mahde
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 183 - Number 52
Year of Publication: 2022
Authors: Abdu-Alkafi Saead Sand, Sultan Senan Mahde
10.5120/ijca2022921938

Abdu-Alkafi Saead Sand, Sultan Senan Mahde . Hop Hubtic Number and Hop Hub Polynomial of Graphs. International Journal of Computer Applications. 183, 52 ( Feb 2022), 1-5. DOI=10.5120/ijca2022921938

@article{ 10.5120/ijca2022921938,
author = { Abdu-Alkafi Saead Sand, Sultan Senan Mahde },
title = { Hop Hubtic Number and Hop Hub Polynomial of Graphs },
journal = { International Journal of Computer Applications },
issue_date = { Feb 2022 },
volume = { 183 },
number = { 52 },
month = { Feb },
year = { 2022 },
issn = { 0975-8887 },
pages = { 1-5 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume183/number52/32278-2022921938/ },
doi = { 10.5120/ijca2022921938 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T01:20:03.848259+05:30
%A Abdu-Alkafi Saead Sand
%A Sultan Senan Mahde
%T Hop Hubtic Number and Hop Hub Polynomial of Graphs
%J International Journal of Computer Applications
%@ 0975-8887
%V 183
%N 52
%P 1-5
%D 2022
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The maximum order of partition of the vertex set V (G) into vertex hop hub sets is called hop hubtic number of G and denoted by h?(G). In this paper the hop hubtic number of some standard graphs was determined. Also bounds for h?(G) were obtained. The hop hub polynomial of a connected graph G was introduced. The hop hub polynomial of a connected graph G of order n is the polynomial Hh(G, x) = |VX(G)| i=hh(G) hh(G, i)xi, where hh(G, i) denotes the number of hop hub sets of G of cardinality i and hh(G) is the hop hub number of G. Finally, the hop hub polynomial of some special classes of graphs was studied.

References
  1. S. Akbari, S. Alikhani and Y. H. Peng, Characterization of graphs using domination polynomial, European J., 31 (2010), 1714-1724.
  2. G. D. Birkhoff and D. C. Lewis, Chromatic polynomials, Trans. Amer. Math. Soc., 60 (1946), 355-451.
  3. E. J. Cockayne, S. T. Hedetniemi, Towards a theory of domination in graphs, Networks 7 (1977), 247261.
  4. E. J. Farrell, A note on the clique polynomial and its relation to other graph polynomials, J. Math. Sci., (Calcutta) 8 (1997), 97-102.
  5. F. Harary, Graph theory, Narosa Publishing House, New Delhi, 2001.
  6. T.W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of domination in graphs, Marcel Dckker, New York, 1998.
  7. S. I. Khalaf, V. Mathad and S. S. Mahde, Hubtic number in graphs, Opuscula Math., 38 (6) (2018), 841–847.
  8. S. S. Mahde and V. Mathad, Hub-integrity polynomial of graphs, TWMS J. App. Eng. Math., 10(2) (2020), 434-442.
  9. S. S. Mahde and A. S. Sand, Hop hub-integrity of graphs, Int. J. Math. And Appl., 9(4)(2021), 91-100.
  10. A. Mowshowitz, The characteristic polynomial of a graph, J. Combin. Theory Ser., B 12 (1972), 177-193.
  11. A. S. Sand, S. S. Mahde, Hop hub number in graphs , submitted.
  12. W. T. Tutte, A contribution to the theory of chromatic polynomials, Canad. J. Math., 6 (1954), 80-91.
  13. R. P. Veettil and T. V. Ramakrishnan, Introduction to hub polynomial of graphs, Malaya Journal of Matematik., 8(4) (2020) 1592-1596.
  14. M. Walsh, The hub number of graphs, Int. J. Math. Comput. Sci., 1 (2006), 117-124.
Index Terms

Computer Science
Information Sciences

Keywords

Hubtic number Hop Hubtic number Hop Hub number Hub polynomial

Powered by PhDFocusTM