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A Paradigmatic Approach to Find Equal Sum Partitions of Zero-Divisors via Complete Graphs
- Source :
- Journal of Chemistry, Vol 2022 (2022)
- Publication Year :
- 2022
- Publisher :
- Wiley, 2022.
-
Abstract
- In computer science and mathematics, a partition of a set into two or more disjoint subsets with equal sums is a well-known NP-complete problem. This is a hard problem and referred to as the partition problem or number partitioning. In this paper, we solve a particular type of NP-complete problem on the set of all zero-divisors of Zn including zero, where Zn is the ring of residue classes of a positive integer n. In this regard, we introduce and investigate quadratic zero-divisor graph in which we build an edge between zero-divisors zi and zj if and only if zi2≡zj2 mod n,i≠j. This is denoted as G⏞2,n. We characterize these graphs in term of complete graphs for classes of integers 2α,pα,2αp,2pα and pq, where α is any positive integer and p,q are odd primes.
Details
- Language :
- English
- ISSN :
- 20909071
- Volume :
- 2022
- Database :
- Directory of Open Access Journals
- Journal :
- Journal of Chemistry
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.61e7313ef64425f9e6a3189a1c20a6b
- Document Type :
- article
- Full Text :
- https://doi.org/10.1155/2022/1587689