Adjacency Matrix and Energy of the Line Graph of $\Gamma(\mathbb{Z}_n)$
Abstract
Let $\Gamma(\mathbb{Z}_n)$ be the zero divisor graph of the commutative ring $\mathbb{Z}_n$ and $L(\Gamma(\mathbb{Z}_n))$ be the line graph of $\Gamma(\mathbb{Z}_n)$. In this paper, we discuss about the neighborhood of a vertex, the neighborhood number and the adjacency matrix of $L(\Gamma(\mathbb{Z}_n))$. We also study Wiener index and energy of $L(\Gamma(\mathbb{Z}_n))$, where $n=pq$, $p^2$ respectively for $p$ and $q$ are primes. Moreover, we give MATLAB coding of our calculations.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2018
- DOI:
- 10.48550/arXiv.1806.08944
- arXiv:
- arXiv:1806.08944
- Bibcode:
- 2018arXiv180608944S
- Keywords:
-
- Mathematics - Combinatorics;
- 05C20;
- 05C25;
- 05C78