Some Families of Elegant and Harmonious Graphs

Abstract

In this paper, we give the following labelings:

1. Elegant labelings of triangular snakes \(\Delta_{n}\) , \(n \equiv 0,1,2 \mod 4\).
2. Near-elegant labeling of triangular snakes \(\Delta_{n}\) when \(n \equiv 3 \mod 4\), which are not elegant.
3. Elegant and near-elegant labelings of some of the theta graphs \(\theta_{n,n}\) when \(n = 1, 2, 3\).
4. Harmonious labelings of helms \(H_n\) when \(n\) is even.