Some Families of Elegant and Harmonious Graphs

Abstract

In this paper, we give the following labelings:

1. Elegant labelings of triangular snakes ${\mathrm{\Delta }}_n$ , $n\equiv 0,1,2\mathrm{mod}4$.
2. Near-elegant labeling of triangular snakes ${\mathrm{\Delta }}_n$ when $n\equiv 3\mathrm{mod}4$, 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.