The Full m Index Sets of P2×Pn
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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/8893804 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832547224093982720 |
|---|---|
| author | Zhizhong Liu Jinmeng Liu Yurong Ji |
| author_facet | Zhizhong Liu Jinmeng Liu Yurong Ji |
| author_sort | Zhizhong Liu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-63b7a46cb0fc426c9fe575a11f5f6367 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-63b7a46cb0fc426c9fe575a11f5f63672025-02-03T06:45:39ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/8893804The Full m Index Sets of P2×PnZhizhong Liu0Jinmeng Liu1Yurong Ji2School of Mechanical and Power EngineeringBasic DepartmentSchool of Mathematics and Information ScienceShiu 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.http://dx.doi.org/10.1155/2023/8893804 |
| spellingShingle | Zhizhong Liu Jinmeng Liu Yurong Ji The Full m Index Sets of P2×Pn Journal of Mathematics |
| title | The Full m Index Sets of P2×Pn |
| title_full | The Full m Index Sets of P2×Pn |
| title_fullStr | The Full m Index Sets of P2×Pn |
| title_full_unstemmed | The Full m Index Sets of P2×Pn |
| title_short | The Full m Index Sets of P2×Pn |
| title_sort | full m index sets of p2 pn |
| url | http://dx.doi.org/10.1155/2023/8893804 |
| work_keys_str_mv | AT zhizhongliu thefullmindexsetsofp2pn AT jinmengliu thefullmindexsetsofp2pn AT yurongji thefullmindexsetsofp2pn AT zhizhongliu fullmindexsetsofp2pn AT jinmengliu fullmindexsetsofp2pn AT yurongji fullmindexsetsofp2pn |