Some New Classes of Harmonious Graphs
Publication Type:Journal Article
Source:Proceedings of the Jangjeon Mathematical Society, The Jangjeon Mathematical Society, Volume 19, Number 2, p.293–299 (2016)
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.