Gaussian Twin Neighborhood Prime Labeling on Fan Digraphs
| Autor: | K Palani, A Shunmugapriya |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Ratio Mathematica, Vol 45, Iss 0 (2023) |
| Druh dokumentu: | article |
| ISSN: | 1592-7415 2282-8214 |
| DOI: | 10.23755/rm.v45i0.973 |
| Popis: | Gaussian integers are complex numbers of the form \gamma=x+iy where x and y are integers and i^2=-1. The set of Gaussian integers is usually denoted by \mathbb{Z}[i]. A Gaussian integer \gamma=a+ib\in\mathbb{Z}[i] is prime if and only if either \gamma=\pm(1\pm i),N(\gamma)= a^2+b^2 is a prime integer congruent to 1(mod4), or \gamma=p+0i or =0+pi where p is a prime integer and |p|\equiv3(mod4). Let D=(V,A) be a digraph with |V|=n. An injective function f:V(D)\rightarrow\left[\gamma_n\right] is said to be a Gaussian twin neighborhood prime labeling of D, if it is both Gaussian in and out neighborhood prime labeling. A digraph which admits a Gaussian twin neighborhood prime labeling is called a Gaussian twin neighborhood prime digraph. In this paper, we introduce some definitions of fan digraphs. Further, we establish the Gaussian twin neighborhood prime labeling in fan digraphs using Gaussian integers. |
| Databáze: | Directory of Open Access Journals |
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