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Abstract
A hypergraph is an extension of a graph in which one edge can connect any number of vertices. In contrary, an edge connects exactly two vertices in a graph.In this paper we introduce hub-hyperpath, hubset and hubnumber of a hypergraph. Also we defined the hubnumber of a different types of hypergraphs and analyze some of its properties. Then the hub number of a hypergraph is compared with its dual hypergraph. Hubset can be useful for various tasks, such as targeted marketing and social networks. Additionally, finding the hub number of a graph is useful in network security, as it helps in identifying nodes that, if compromised, could have a significant impact on the overall network.
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References
- Bretto, A., Hypergraph Theory, Springer International Publishing Switzerland, ISBN 978-3-319-00079-4, 2013.
- Berge, C. J., Hypergraphs, North-Holland Mathematical Library, Vol.15, ISBN: 0-444-87489-5, Elsevier Science Publishers B.V., 1989.
- Walsh, M., The Hub Number of a Graph, International Journal of Mathematics and Computer Science, ISSN 1814-0424, 1 (2006), 117-124,.
- Khalaf, S. I., Mathad, V., Mahde, S. S., Hub and global hub numbers of a graph, Proceedings of the Jangjeon Mathematical Society, 23(2) 2020, 231 - 239.
References
Bretto, A., Hypergraph Theory, Springer International Publishing Switzerland, ISBN 978-3-319-00079-4, 2013.
Berge, C. J., Hypergraphs, North-Holland Mathematical Library, Vol.15, ISBN: 0-444-87489-5, Elsevier Science Publishers B.V., 1989.
Walsh, M., The Hub Number of a Graph, International Journal of Mathematics and Computer Science, ISSN 1814-0424, 1 (2006), 117-124,.
Khalaf, S. I., Mathad, V., Mahde, S. S., Hub and global hub numbers of a graph, Proceedings of the Jangjeon Mathematical Society, 23(2) 2020, 231 - 239.