A Vertex Code of Designed Distance 𝑑𝐻 and its Graph G

Sreedevi S. L; N. Suresh Babu

doi:https://doi.org/10.14445/22315373/IJMTT-V68I6P518

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 6 | Year 2022 | Article Id. IJMTT-V68I6P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I6P518

A Vertex Code of Designed Distance 𝑑𝐻 and its Graph G

Sreedevi S. L, N. Suresh Babu

Received	Revised	Accepted	Published
03 May 2022	16 Jun 2022	25 Jun 2022	30 Jun 2022

Abstract

Matrices associated with the graphs were considered as a good tool to construct codes from graphs with desirable properties. We introduced a new binary code – the vertex code 𝐶 from a given graph 𝐺, depending on the degree of the vertices of 𝐺, in such a way that the vertex polynomial of 𝐺 is same as the weight enumerator of 𝐶 in [3]. A detailed study on the properties of the vertex code was carried out in[4]. In this paper we revise the vertex code given there in with the purpose of enhancing the error correcting capability of the code and try to generalize the nature of the graph for a given code of specified size and distance.

Keywords

Graph, Vertex degree, Degree sequence, Arithmetic sequence, Error correcting codes, Vertex code.

References

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Citation :

Sreedevi S. L, N. Suresh Babu, "A Vertex Code of Designed Distance 𝑑𝐻 and its Graph G," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 6, pp. 149-155, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I6P518