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N. Annamalai

Publications and source records attributed to N. Annamalai.

10 recordsLinked to original sources
arXiv2026

Graph Theoretic and Spectral Properties of the Zero-Divisor Graph of $\mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p$

In this article, we study the zero-divisor graph of the commutative ring with identity $R= \mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p,$ where $u^2 = 0, v^2 = 0, uv = vu$ and $p$ is an odd prime. We determine several graph-theoretic properties associated with the zero-divisor graph $Γ(R),$ including the clique number, chromatic number, vertex connectivity, edge connectivity, diameter and girth. In addition, we compute certain topological indices of the graph $Γ(R).$ Furthermore, we find the eigenvalues, energy and spectral radius of the adjacency matrix, the Laplacian matrix and the Eccentricity matrix of the zero-divisor graph $(Γ(R).$

math.RA↗
arXiv2022

On Zero-Divisor Graph of the ring $\mathbb{F}_p+u\mathbb{F}_p+u^2 \mathbb{F}_p$

In this article, we discussed the zero-divisor graph of a commutative ring with identity $\mathbb{F}_p+u\mathbb{F}_p+u^2 \mathbb{F}_p$ where $u^3=0$ and $p$ is an odd prime. We find the clique number, chromatic number, vertex connectivity, edge connectivity, diameter and girth of a zero-divisor graph associated with the ring. We find some of topological indices and the main parameters of the code derived from the incidence matrix of the zero-divisor graph $Γ(R).$ Also, we find the eigenvalues, energy and spectral radius of both adjacency and Laplacian matrices of $Γ(R).$

cs.IT↗
arXiv2022

Minimum Roman Dominating Distance Energy of a Graph

In this correspondence, we introduced the concept of minimum roman dominating distance energy $E_{RDd}(G)$ of a graph $G$ and computed minimum roman dominating distance energy of some standard graphs. Also, we discussed the properties of eigenvalues of a minimum roman dominating distance matrix $A_{RDd}(G).$ Finally, we derived the Upper and lower bounds for $E_{RDd}(G).$

math.CO↗
arXiv2021

Additive Tridiagonal Codes over $\mathbb{F}_{4}$

In this paper, we introduce a additive Tridiagonal and Double-Tridiagonal codes over $\mathbb{F}_4$ and then we study the properties of the code. Also, we find the number of additive Tridiagonal codes over $\mathbb{F}_4.$ Finally, we study the applications of Double-Tridiagonal codes to secret sharing scheme based on matrix projection.

cs.IT↗
arXiv2020

Linear Codes from Incidence Matrices of Unit Graphs

In this paper, we examine the binary linear codes with respect to Hamming metric from incidence matrix of a unit graph $G(\mathbb{Z}_{n})$ with vertex set is $\mathbb{Z}_{n}$ and two distinct vertices $x$ and $y$ being adjacent if and only if $x+y$ is unit. The main parameters of the codes are given.

cs.IT↗
arXiv2020

Codes from the Incidence Matrices of a zero-divisor Graphs

In this paper, we examine the linear codes with respect to the Hamming metric from incidence matrices of the zero-divisor graphs with vertex set is the set of all non-zero zero-divisors of the ring $\mathbb{Z}_n$ and two distinct vertices being adjacent iff their product is zero over $\mathbb{Z}_n.$ The main parameters of the codes are obtained.

cs.IT↗
arXiv2020

Exponent of Cyclic Codes over $\mathbb{F}_q$

In this article, we introduce and study the concept of the exponent of a cyclic code over a finite field $\mathbb{F}_q.$ We give a relation between the exponent of a cyclic code and its dual code. Finally, we introduce and determine the exponent distribution of the cyclic code.

cs.IT↗
arXiv2016

Relative two-weight $\mathbb{Z}_2 \mathbb{Z}_4$-additive Codes

In this paper, we study a relative two-weight $\mathbb{Z}_2 \mathbb{Z}_4$-additive codes. It is shown that the Gray image of a two-distance $\mathbb{Z}_2 \mathbb{Z}_4$-additive code is a binary two-distance code and that the Gray image of a relative two-weight $\mathbb{Z}_2 \mathbb{Z}_4$-additive code, with nontrivial binary part, is a linear binary relative two-weight code. The structure of relative two-weight $\mathbb{Z}_2 \mathbb{Z}_4$-additive codes are described. Finally, we discussed permutation automorphism group of a $\mathbb{Z}_2 \mathbb{Z}_4$-additive codes.

cs.IT↗
arXiv2016

The Structure of Z_2[u]Z_2[u, v]-additive Codes

In this paper, we study the algebraic structure of Z_2[u]Z_2[u, v]-additive codes which are Z_2[u, v]-submodules where u^2 = v^2 = 0 and uv = vu. In particular, we determine a Gray map from Z_2[u]Z_2 [u, v] to Z_2^{2α+8\b{eta}} and study generator and parity check matrices for these codes. Further we study the structure of Z_2[u]Z_2[u, v]-additive cyclic codes and constacyclic codes.

cs.IT↗