On $t$-Perfect Codes in Corona Product of Graphs

Abstract

A perfect code in a graph is a subset of a vertex set with the property that each vertex is adjacent to exactly one vertex in the subset. The corona product of two graphs $G$ and $H$ is the graph $G\circ H$ is obtained by taking one copy of $G$, called the centre graph and $\left|V\left(G\right)\right|$ copies of $H$, called the outer graph and by joining each vertex of the i\textsuperscript{th} copy of $H$ to the i\textsuperscript{th} vertex of $G$, where $1\le i\le \left|V\left(G\right)\right|$. The aim of this paper is to discuss the sufficient condition for the existence of $t$-perfect codes in corona product of two graphs.