Abstract
In this paper, we present a new family of graphs called Marigold graphs and introduce a new labelling method similar to the anti-magic labelling. The Marigold graph is generated from any number of copies of fully binary trees which are going through concentric circles. All copies of trees are connected to a middle vertex and the height of the Marigold graph is increasing with n concentric circles. One copy is considered as one petal in the marigold graph. A Marigold graph with copies (petals) and height (number of concentric circles) k is M nk denoted by . The labelling method is defined as follows: A graph with ‘m’ edges and ‘n’ vertices is labelled as an injection from the set of edges to the integers {1, …, x} such that all ‘n’ vertex sums are pairwise distinct, where the vertex sum is the sum of labels of all edges incident with that vertex. In our work, for edge labelling, we consider the petals one by one and denote the rth edge at kth level as ekr , and define a function to label edges of the first petal. Then define the new labelling method for other petals, such that for nth petal, edge labelling is starting with Jn–1 + 1 (where Jn–1 is the summation of all edge values in (n –1)th petal, ∑i=1m (n–1, i) = Jn–1 and continue the labelling as a monotonically increasing sequence. We discuss some illustrative examples that might be used for studying the Anti-magic like labelling of Marigold graphs.