SD-prime cordial labeling of alternate k-polygonal snake of various types

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-4015

Keywords:

SD-prime cordial graph, Triangular snake, Alternate quadrilateral snake, n-polygonal snake, Alternate k-polygonal snake

Abstract

Let f : V (G) → {1, 2,..., |V (G)|} be a bijection, and let us denote S = f(u) + f(v) and D = |f(u) − f(v)| for every edge uv in E(G). Let f' be the induced edge labeling, induced by the vertex labeling f, defined as f' : E(G) → {0, 1} such that for any edge uv in E(G), f' (uv)=1 if gcd(S, D)=1, and f' (uv)=0 otherwise. Let ef' (0) and ef' (1) be the number of edges labeled with 0 and 1 respectively. f is SD-prime cordial labeling if |ef' (0) − ef' (1)| ≤ 1 and G is SD-prime cordial graph if it admits SD-prime cordial labeling. In this paper, we have discussed the SD-prime cordial labeling of alternate k-polygonal snake graphs of type-1, type-2 and type-3.

Author Biographies

Udayan Prajapati, St. Xavier’s College (Autonomous).

Dept. of Mathematics.

Anit Vantiya, Gujarat University,

Dept. of Mathematics, Research Scholar.

 K. K. Shah Jarodwala Maninagar Science College, Assistant Professor,

References

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Published

2021-04-27

How to Cite

[1]
U. Prajapati and A. Vantiya, “SD-prime cordial labeling of alternate k-polygonal snake of various types”, Proyecciones (Antofagasta, On line), vol. 40, no. 3, pp. 619-634, Apr. 2021.

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Section

Artículos