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 Pn and cycles Cn, namely, Pn⊙Cm. A graph is said to be logical labeling if it has a 0−1 labeling that satisfies certain properties. The corona G1⊙G2 of two graphs G1 (with n1 vertices and m1 edges) and G2 (with n2 vertices and m2 edges) is defined as the graph formed by taking one copy of G1 and n1 copies of G2 and then connecting the ith vertex of G1 with an edge to every vertex in the ith copy of G2.