Cartesian Product of Quadratic Residue Graphs

doi:10.13189/ms.2023.110222

Journals Information

Mathematics and Statistics Vol. 11(2), pp. 434 - 439
DOI: 10.13189/ms.2023.110222
Reprint (PDF) (589Kb)

Cartesian Product of Quadratic Residue Graphs

Shakila Banu P. ¹, Suganthi T. ²^,*
¹ Assistant Professor, Department of Mathematics, Vellalar College for Women, India
² B.T.Assistant of Mathematics, Govt. Higher Secondary School, India

ABSTRACT

Rezaei [7], who introduced the first simple graph G, defined it as a quadratic residue graph modulo n if its vertex set is reduced, a residue system modulo n such that two different vertices a and b are nearby, and (mod n). This initiates to study the present article, here we introduce a cartesian product of quadratic residue graphs , where m and n are either prime or composite, and G_m and H_n are quadratic residue graphs, respectively. The aforementioned work suggests and evaluates the regular graphs that are produced from graph F and its adjacency matrix. In addition, we define and examine their generating matrices with the help of adjacency matrix of F. Also, in this article we define three linear codes that are taken from the graph F and the parameters of codes denotes [N, k, d], where N denotes length, k denotes the dimension which is taken from the number of vertices and d denotes the distance which is taken from the minimum degree. Moreover, we also introduce an encoding and decoding algorithm for the graph using binary bits which is illustrated with a suitable example. Finally, we test the error correction capability of the code by using sphere packing bounds.

KEYWORDS
Cartesian Product, Quadratic Residue, Graphs, Regular Graph, Encoding and Decoding

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Shakila Banu P. , Suganthi T. , "Cartesian Product of Quadratic Residue Graphs," Mathematics and Statistics, Vol. 11, No. 2, pp. 434 - 439, 2023. DOI: 10.13189/ms.2023.110222.

(b). APA Format:
Shakila Banu P. , Suganthi T. (2023). Cartesian Product of Quadratic Residue Graphs. Mathematics and Statistics, 11(2), 434 - 439. DOI: 10.13189/ms.2023.110222.