Euler ’ s Phi Function and Graph Labeling
نویسنده
چکیده
A graph G(V,E) with vertex set V is said to have a prime labeling if there exist a bijection f : V (G) → {1, 2, . . . , |V |} such that for each edge xy ∈ E(G), f(x) and f(y) are relatively prime. It becomes an interesting problem to investigate the maximum possible edges that can be constructed in a graph with n vertices having prime labeling property. We interpret this problem in number theory to find total number of relatively prime pair of integers in the set {1, 2, 3, . . . , n} and prove an interesting result connecting with Euler’s phi function φ(n). Further an algorithmic approach is established for prime labeling for the class of maximal planar graph Pln using the number theory techniques. Mathematics Subject Classification: 05C78
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