Hop Hub-Integrity of Graphs

# Sultan Senan Mahde1 and Abdu-Alkafi Saead Sand1

1Department of Mathematics, Faculty of Education and Science, University of Al-Baydha, Yemen.

Abstract: The concept of hop hub-integrity is introduced as a new measure of the stability of a graph $G$ and it is defined as $H_hI(G) = min \{|S| + m(G - S)\},$ where $S$ is hop hub set and $m(G - S)$ is the order of a maximum component of $(G - S)$. In this paper, the hop hub-integrity of some graphs is obtained.The relations between hop hub-integrity and other parameters are determined.
Keywords: Hub number, Hop hub number, Domination number, Connected hub number, Connected domination number.

Cite this article as: S. S. Mahde and A. S. Sand, Hop Hub-Integrity of Graphs, Int. J. Math. And Appl., vol. 9, no. 4, 2021, pp. 91-100.

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