Abstract

Binary codes from graphs have been studied widely since 1960’s. Matrices associated with the graphs were considered as a good tool to construct codes from graphs. Incidence matrix, Adjacency matrix, cut set matrix, circuit matrix etc. were widely used to construct codes with desirable properties. Here we introduce 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.

Keywords

References

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[3] G. Suresh Singh, ‘Graph Theory’, PHI Learning Private Limited, New Delhi, 2010.