The Full m Index Sets of P2×Pn

Abstract

Shiu and Kwong (2008) studied the full friendly index set of P2×Pn, which only addressed the cases where m=0 or 1. In this paper, we significantly extend their work by determining the full m index set MP2×Pn for all values of m. Our key approach is to utilize graph embedding and recursion methods to deduce MP2×Pn for general m. In particular, we embed small graphs like C4 and K2 into P2×Pn and apply recursive techniques to prove the main results. This work expands the scope of previous graph labeling studies and provides new insights into determining the full m index set of product graphs. Given the broad range of applications for labeled graphs, this research can potentially impact fields like coding theory, communication network design, and more.