Missing Numbers in K-Graceful Graphs

Abstract

The generalization of graceful labeling is termed as-graceful labeling. In this paper it has been shown that , is-graceful for any (set of natural numbers) and some results related to missing numbers for-graceful labeling of cycle , comb , hairy cycle and wheel graph have been discussed.

ON k-GRACEFUL LABELING OF SOME GRAPHS

“…Maheo and Thuillier [10] have shown that cycle C n is k-graceful if and only if either n ≡ 0 or 1(mod4) with k even and k ≤ (n − 1)/2 or n ≡ 3(mod4) with k odd and k ≤ (n 2 − 1)/2, while P. Pradhan and et al [11] have shown that cycle C n , n ≡ 0(mod4) is k-graceful for all k ∈ N (set of natural numbers). Maheo and Thuillier [10] have also proved that the wheel graph W 2k+1 is k-graceful and conjecture that W 2k is k-graceful when k ̸ = 3 or k ̸ = 4.…”