Abstract
Absolutely harmonious labelingf is an injection from the vertex set of a graph G with q edges to the set {0,1,2,…,q-1}, if each edge uv is assigned f(u)+f(v) then the resulting edge labels can be arranged as {a_0,a_1 a_2,…,a_(q-1)} where a_i=q-ior q+i,0≤ i≤ q-1.However, when G is a tree one of the vertex labels may be assigned to exactly two vertices. A graph which admits Absolutely harmonious labeling is called absolutely harmonious graph. In this paper, we study absolutely harmonious labeling of ring sum of a graph with star graph.
Keyword
Harmonious labelling, Absolutely harmonious labelling, Star graph, Traingular ladder, Jelly Fish, Jewel graph, P¬n2, Globe graph.
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