On the cordial labeling of certain trigraphs

Mohammad Hailat

Abstract


Let G be a graph that has n vertices and m edges. Let f: V(G) → {1,2,..., k} be a function that assigns to each vertex v ∈ G a positive integer f(v) ∈ {1,2,..., k}. We assign to each edge uv ∈ E(G) a label which is the gcd(f(u), f(v)). The function f is called k-prime cordial labeling of G if |vf(i) − vf(j)| ≤ 1 for all i, j ∈ {1,2,..., k} and |ef(0) − ef(1)| ≤ 1, where vf(i) denotes the number of vertices labeled with i, ef(1) and ef(0) denote the number of edges labeled with 1 and not labeled with 1, respectively. In this paper, we introduce the concept of trigraph of a graph G, T3(G), and we show that the trigraph of a path Pn, T3(Pn), and the trigraph of a cycle Cn, T3(Cn) are 4-prime cordial graphs.

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Published: 2021-08-23

How to Cite this Article:

Mohammad Hailat, On the cordial labeling of certain trigraphs, J. Math. Comput. Sci., 11 (2021), 6936-6948

Copyright © 2021 Mohammad Hailat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

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