Call for Paper - January 2024 Edition
IJCA solicits original research papers for the January 2024 Edition. Last date of manuscript submission is December 20, 2023. Read More

Hop Hubtic Number and Hop Hub Polynomial of Graphs

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2022
Abdu-Alkafi Saead Sand, Sultan Senan Mahde

Abdu-Alkafi Saead Sand and Sultan Senan Mahde. Hop Hubtic Number and Hop Hub Polynomial of Graphs. International Journal of Computer Applications 183(52):1-5, February 2022. BibTeX

	author = {Abdu-Alkafi Saead Sand and Sultan Senan Mahde},
	title = {Hop Hubtic Number and Hop Hub Polynomial of Graphs},
	journal = {International Journal of Computer Applications},
	issue_date = {February 2022},
	volume = {183},
	number = {52},
	month = {Feb},
	year = {2022},
	issn = {0975-8887},
	pages = {1-5},
	numpages = {5},
	url = {},
	doi = {10.5120/ijca2022921938},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}


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.


  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.


Hubtic number, Hop Hubtic number, Hop Hub number, Hub polynomial