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Hop Hubtic Number and Hop Hub Polynomial of Graphs

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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 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

@article{10.5120/ijca2022921938,
	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 = {http://www.ijcaonline.org/archives/volume183/number52/32278-2022921938},
	doi = {10.5120/ijca2022921938},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, 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.

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Keywords

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