A Novel Problem to Solve the Logically Labeling of Corona between Paths and Cycles

Abstract

In this study, we propose a new kind of graph labeling which we call logic labeling and investigate the logically labeling of the corona between paths $P_n$ and cycles $C_n$ , namely, $P_n\odot C_m$ . A graph is said to be logical labeling if it has a $0-1$ labeling that satisfies certain properties. The corona $G_1\odot G_2$ of two graphs $G_1$ (with $n_1$ vertices and $m_1$ edges) and $G_2$ (with $n_2$ vertices and $m_2$ edges) is defined as the graph formed by taking one copy of $G_1$ and $n_1$ copies of $G_2$ and then connecting the $i^{\text{th}}$ vertex of $G_1$ with an edge to every vertex in the $i^{\text{th}}$ copy of $G_2$ .