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pendant domination
Open AccessArticleOn Pendant Domination Polynomial in the Corona of Some Graphs
Ariel C. Pedrano* and Christine R. Giganto
Annals of Communications in Mathematics 2025,
8 (4),
442-450
DOI: https://doi.org/10.62072/acm.2025.080402
ABSTRACT. A dominating set \( S \) in \( G \) is called a pendant dominating set if \( \langle S \rangle \) contains at least one pendant vertex. The minimum cardinality of a pendant dominating set is called the pendant domination number, denoted by \( \gamma_{pe}(G) \). The pendant domination polynomial of \( G \) is denoted by \( D_{pe}(G,x) \) and is defined as\[D_{pe}(G,x)=\sum_{i=\gamma_{pe}(G)}^{n} d_{pe}(G,i)\,x^{i},\]where \( d_{pe}(G,i)x^{i} \) is the number of pendant dominating sets of size \( i \). In this paper, we obtained the pendant domination number and pendant domination polynomial of the corona of some graphs, namely, \( P_m \circ K_n \), \( C_m \circ K_n \), and \( K_m \circ K_n \).




