Odd Graceful Labeling of Cycle with Parallel Pk Chords
نویسندگان
چکیده
A graph labeling is an assignment of integers to the vertices (or) edges or both subject to certain conditions. Graceful labeling was introduced by Rosa [6] while the concept of odd graceful labeling was introduced by Gnanajothi [2]. A Graph G (V, E), |V(G)| = p, |E(G)| = q is said to be odd graceful if there is an injection from V(G) to {0, 1, 2, .... 2q-1} such that when each edge xy is assigned the label |f(x) f(y)| the resulting edge labels are distinct and are in the set {1, 3, 5, ... 2q-1}. In this paper we prove theodd gracefulness of every even cycle Cn, n ≥ 6 with parallel Pk chords for k = 3, 5 and also prove the odd gracefulness of every odd cycle Cnn≥ 7 with parallel Pkchords for k = 2,4 after the removal of 2 edges from the cycle Cn.
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