Perfect domination polynomial of homogeneous caterpillar graphs and of full binary trees
type: Item
instance of: scholarly article
title: Perfect domination polynomial of homogeneous caterpillar graphs and of full binary trees
zbMATH Open document ID: 1489.05112
DOI: 10.1134/S0001434622010333
author: Temesgen Engida Yimer
author: J. Baskar Babujee
published in: Mathematical Notes
publication date: 2022-03-14T00:00:00Z
review text: 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 \(v\in V(G)\setminus S\) is adjacent to exactly one vertex in \(S\). The perfect domination number \(\gamma_{pf}(G)\) is the minimal cardinality of perfect dominating sets in \(G\). Let \(D_{pf}(G, i)\) be the set of perfect dominating sets of \(G\) with cardinality \(i\) and \(d_{pf}(G, i)=|D_{pf}(G, i)|\). The perfect domination polynomial of \(G\) is defined as \(D_{pf}(G,x)=\sum_{i=\gamma_{pf}(G)}^n d_{pf}(G,i) x^i\), where \(d_{pf}(G, i)\) is the number of perfect dominating sets of \(G\) of size \(i\). In this paper, the authors determine the perfect domination polynomial of homogeneous caterpillars and of full binary trees.
reviewed by: Baoyindureng Wu
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C31
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 7488505
zbMATH Keywords: perfect domination
zbMATH Keywords: perfect domination polynomial
zbMATH Keywords: caterpillars
zbMATH Keywords: binary trees
MaRDI profile type: Publication
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full work available at URL: s0001434622010333
OpenAlex ID: W4213451048
description: scientific article; zbMATH DE number 7488505