F-GEOMETRIC MEAN LABELING OF SOME ... - Kjm.pmf.kg.ac.rs
F-GEOMETRIC MEAN LABELING OF SOME ... - Kjm.pmf.kg.ac.rs
F-GEOMETRIC MEAN LABELING OF SOME ... - Kjm.pmf.kg.ac.rs
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
178 A. DURAI BASKAR, S. AROCKIARAJ AND B. RAJENDRANand⎧⎪ f(v i )+2 ⎨f(v i ′ ) = f(v i )−2⎪ f(v i )−2 ⎩f(v i )+2The induced edge labeling is as follows:1 ≤ i ≤ ⌊ n⌊ 2⌋−1 and i is oddn⌋2 +1 ≤ i ≤ n and i is odd1 ≤ i ≤ ⌊ n⌋ 2⌋and i is even+2 ≤ i ≤ n and i is even.⌊ n2f ∗ (u i u i+1 ) = 2i, for 1 ≤ i ≤ n−1,f ∗ (u i u ′ i ) = 2i−1, for 1 ≤ i ≤ n,⌊ nf ∗ (v i v i+1 ) = 2n−1+4i, for 1 ≤ i ≤ ,⌊2⌋nf ∗ (v n+1−i v n−i ) = 2n+4i, for 1 ≤ i ≤ −1,2⌋and⎧⎪ f(v i ) ⎨f ∗ (v i v i ′ ) = f(v i )−2⎪ f(v i )−2 ⎩f(v i )1 ≤ i ≤ ⌊ n⌊ 2⌋−1 and i is oddn⌋2 +1 ≤ i ≤ n and i is odd1 ≤ i ≤ ⌊ n⌋ 2⌋and i is even+2 ≤ i ≤ n and i is even⌊ n2f ∗ (u i+1 v i ) = 2n, for i =⌊ n2⌋.Case (ii) n ≡ 1(mod 4).We define f : V(G⊙K 1 ) → {1,2,3,...,4n} as follows:andf(u i ) = 2i, for 1 ≤ i ≤ n,f(u ′ i) = 2i−1, for 1 ≤ i ≤ n,{ ⌊2n−3+4i 1 ≤ i ≤n⌋f(v i ) = 2 +1 and i is odd2n−1+4i 1 ≤ i ≤ ⌊ n2⌋and i is even,{ ⌊2n−2+4i 1 ≤ i ≤n⌋f(v n+1 −i) = 2 and i is odd2n+4i 1 ≤ i ≤ ⌊ n2⌋and i is even⎧⎪ f(v ⎨ i )+2f(v i ′ ) = f(v i )+1⎪ f(v ⎩ i )+2f(v i )−2The induced edge labeling is as follows:1 ≤ i ≤ ⌊ n2⌋and i is oddi = ⌊ n⌊ 2⌋+1 and i is oddn⌋2 +3 ≤ i ≤ n and i is odd1 ≤ i ≤ n and i is even.f ∗ (u i u i+1 ) = 2i, for 1 ≤ i ≤ n−1,f ∗ (u i u ′ i ) = 2i−1, for 1 ≤ i ≤ n,⌊ nf ∗ (v i v i+1 ) = 2n−1+4i, for 1 ≤ i ≤ ,⌊2⌋nf ∗ (v n+1−i v n−i ) = 2n+4i, for 1 ≤ i ≤ ,2⌋