On b-edge consecutive edge labeling of some regular tree - Kiki Ariyanti Sugeng; Denny R. Silaban (Indonesian Combinatorial Society (InaCombS), 2020)
Let G = (V, E) be a finite (non-empty), simple, connected and undirected graph, where V and E are the sets of vertices and edges of G. An edge magic total labeling is a bijection α from V ∪ E to the integers 1, 2, . . . , n + e, with the property that for every xy ∈ E, α(x) + α(y) + α(xy) = k, for some constant k. Such a labeling is called a b-edge consecutive edge magic total if α(E) = b + 1, b + 2, . . . , b + e. In this paper, we proved that several classes of regular trees, such as regular caterpillars, regular firecrackers, regular caterpillar-like trees, regular path-like trees, and regular banana trees, have a b-edge consecutive edge magic labeling for some 0 < b < |V |.