Perfect codes in some products of graphs
oleh: Samane Bakaein, Mostafa Tavakoli, Freydoon Rahbarnia
| Format: | Article |
|---|---|
| Diterbitkan: | Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 2021-04-01 |
Deskripsi
<p class="p1">A <em>r</em>-perfect code in a graph <em>G</em> = (<em>V</em>(<em>G</em>),<em>E</em>(<em>G</em>)) is a subset <em>C</em> of <em>V</em>(<em>G</em>) for which the balls of radius <em>r</em> centered at the vertices of <em>C</em> form a partition of <em>V</em>(<em>G</em>). In this paper, we study the existence of perfect codes in corona product and generalized hierarchical product of graphs where the cardinality of <em>U</em> is equal to one or two. Also, we give some examples as applications of our results.</p>