For a finite graph G of order p and size q, let V(G) and E(G) denote its vertex and edge set respectively. A harmonious labeling of a connected graph G is an injective function λ: V(G) → Z<sub>q</sub> such that the induced edge function λ∗: V(G) → Z<sub>q</sub> defined as λ∗(xy) = λ (x) + λ(y)]modq for each edge xy ϵ E(G) is a bijection whenever G is not a tree. If G is a tree, exactly one label may be used on two vertices. In this note we report some new classes of harmonious graphs.
K. Abhishek, “Some New Classes of Harmonious Graphs”, Proceedings of the Jangjeon Mathematical Society, vol. 19, pp. 293–299, 2016.