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Ural Mathematical Journal, 2021, Volume 7, Issue 2, Pages 121–135
DOI: https://doi.org/10.15826/umj.2021.2.009
(Mi umj154)
 

On hop domination number of some generalized graph structures

S. Shanmugavelan, C. Natarajan

Srinivasa Ramanujan Centre, SASTRA Deemed to be University
References:
Abstract: A subset $ H \subseteq V (G) $ of a graph $G$ is a hop dominating set (HDS) if for every ${v\in (V\setminus H)}$ there is at least one vertex $u\in H$ such that $d(u,v)=2$. The minimum cardinality of a hop dominating set of $G$ is called the hop domination number of $G$ and is denoted by $\gamma_{h}(G)$. In this paper, we compute the hop domination number for triangular and quadrilateral snakes. Also, we analyse the hop domination number of graph families such as generalized thorn path, generalized ciliates graphs, glued path graphs and generalized theta graphs.
Keywords: hop domination number, snake graphs, theta graphs, generalized thorn path.
Funding agency Grant number
Fund for Improvement of S&T infrastructure in universities & higher educational institutions (FIST) SR/FST/MSI-107/2015(c)
Department of Science and Technology, Government of India for the financial support to the Department of Mathematics, SASTRA Deemed to be University under FIST Programme - Grant No.: SR/FST/MSI-107/2015(c).
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Document Type: Article
Language: English
Citation: S. Shanmugavelan, C. Natarajan, “On hop domination number of some generalized graph structures”, Ural Math. J., 7:2 (2021), 121–135
Citation in format AMSBIB
\Bibitem{ShaNat21}
\by S.~Shanmugavelan, C.~Natarajan
\paper On hop domination number of some generalized graph structures
\jour Ural Math. J.
\yr 2021
\vol 7
\issue 2
\pages 121--135
\mathnet{http://mi.mathnet.ru/umj154}
\crossref{https://doi.org/10.15826/umj.2021.2.009}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4358918}
\elib{https://elibrary.ru/item.asp?id=47556646}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85124350260}
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