The Full m Index Sets of P 2 × P n

Shiu and Kwong (2008) studied the full friendly index set of P 2 × P n , 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 M P 2 × P n for all values of m . Our key approach is to utilize graph embedding and recursi...

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Bibliographic Details
Published inJournal of mathematics (Hidawi) Vol. 2023; pp. 1 - 8
Main Authors Liu, Zhizhong, Liu, Jinmeng, Ji, Yurong
Format Journal Article
LanguageEnglish
Published 20.12.2023
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Summary:Shiu and Kwong (2008) studied the full friendly index set of P 2 × P n , 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 M P 2 × P n for all values of m . Our key approach is to utilize graph embedding and recursion methods to deduce M P 2 × P n for general m . In particular, we embed small graphs like C 4 and K 2 into P 2 × P n 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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2023/8893804