Abstract

Let 𝐺 be a 𝑝, 𝑞 graph and 𝑓: 𝑉(𝐺) → {1,2, … , 𝑝 + 𝑞 − 1, 𝑝 + 𝑞 +2} be an injection. For each edge 𝑒 = 𝑢𝑣, the induced edge labeling 𝑓 ∗ is defined as follows: 𝑓 ∗ 𝑒 = 𝑓 𝑢 − 𝑓(𝑣) 2 𝑖𝑓 𝑓 𝑢 − 𝑓 𝑣 𝑖𝑠 𝑒𝑣𝑒𝑛 𝑓 𝑢 −𝑓(𝑣) + 1 2 𝑖𝑓 𝑓 𝑢 − 𝑓 𝑣 𝑖𝑠 𝑜𝑑𝑑 Then 𝑓 is called Near Skolem difference mean labeling if 𝑓 ∗ (𝑒) are all distinct and from 1,2,3, … . 𝑞 . A graph that admits a Near Skolem difference mean labeling is called a Near Skolem difference mean graph. In this paper, we investigate near Skolem difference mean labelling of some special types of trees like the banana tree, the coconut tree, the 𝐻 − graph, the lily graph, the jelly fish graph and the graph T 𝐾1,𝑛1 ◦𝐾1,𝑛2 ◦◦◦𝐾1,𝑛𝑚

Keywords

References

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