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Matematicheskie Zametki, 2022, Volume 111, Issue 2, paper published in the English version journal (Mi mzm13227)  

This article is cited in 1 scientific paper (total in 1 paper)

Papers published in the English version of the journal

Perfect Domination Polynomial of Homogeneous Caterpillar Graphs and of Full Binary Trees

Temesgen Engida Yimer, J. Baskar Babujee

Department of Mathematics, Anna University, MIT Campus, Chennai, 600044 India
Citations (1)
Abstract: Let $G=(V,E)$ be a simple graph of order $n$. A set $S \subseteq V(G)$ is a perfect dominating set of a graph $G$ if every vertex $v\in V(G)-S$ is adjacent to exactly one vertex in $S$. That is, every vertex outside $S$ has exactly one neighbor in $S$. Every graph $G$ has at least the trivial perfect dominating sets consisting of all vertices in $G$. The perfect domination number $\gamma_{pf} (G)$ is the minimal cardinality of dominating sets in $G$. Let $D_{pf} (G,i)$ be the family of perfect dominating sets for a graph $G$ with cardinality $i$ and $d_{pf} (G,i)= |D_{pf} (G,i)|$. The perfect domination polynomial of a graph $G$ of order $n$ is
$$ D_{pf} (G,x)=\sum_{i=\gamma_{pf}(G)}^{n} d_{pf}(G,i)x^n, $$
where $d_{pf} (G,i)$ is the number of perfect dominating sets of $G$ of size $i$. In this paper, we studied the perfect domination polynomial $D_{pf} (G,x)$ of homogeneous caterpillar graphs and of full binary trees.
Keywords: perfect domination sets, perfect domination polynomial, homogeneous caterpillar graphs, full binary tree, corona graph.
Funding agency Grant number
Minister of Science and Higher Education of the Federal Democratic Republic of Ethiopia
The authors wish to acknowledge the financial support to the first author to carry out the research work provided by the Minister of Science and Higher Education of the Federal Democratic Republic of Ethiopia.
Received: 16.07.2021
English version:
Mathematical Notes, 2022, Volume 111, Issue 2, Pages 297–304
DOI: https://doi.org/10.1134/S0001434622010333
Bibliographic databases:
Document Type: Article
Language: English
Citation: Temesgen Engida Yimer, J. Baskar Babujee, “Perfect Domination Polynomial of Homogeneous Caterpillar Graphs and of Full Binary Trees”, Math. Notes, 111:2 (2022), 297–304
Citation in format AMSBIB
\Bibitem{YimBab22}
\by Temesgen Engida Yimer, J.~Baskar Babujee
\paper Perfect Domination Polynomial of Homogeneous
Caterpillar Graphs and of Full Binary Trees
\jour Math. Notes
\yr 2022
\vol 111
\issue 2
\pages 297--304
\mathnet{http://mi.mathnet.ru/mzm13227}
\crossref{https://doi.org/10.1134/S0001434622010333}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4392538}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85125503318}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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