Perfect codes in some products of graphs

Samane Bakaein, Mostafa Tavakoli, Freydoon Rahbarnia


A r-perfect code in a graph G = (V(G),E(G)) is a subset C of V(G) for which the balls of radius r centered at the vertices of C form a partition of V(G). In this paper, we study the existence of perfect codes in corona product and generalized hierarchical product of graphs where the cardinality of U is equal to one or two. Also, we give some examples as applications of our results.


graph, perfect code, corona product, hierarchical product, generalized hierarchical product

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