| Abstrakt: |
Let Ir (Km,n) denote a r- crown of a complete bipartite graph Km,n, obtained by adding r hanged edges to each vertex of Km,n. Ma kejie conjectured that 1-crown of complete bipartite graph Km,n (m ≤ n) is k-graceful graph for k ≥ 2. The conjecture has been shown true when m = 1, 2, 3, 4 for arbitrary n ≥ m and r ≥ 2. In this paper we discuss the k-gracefulness of r-crown Ir (Km,n) (m ≤ n, r ≥ 2) for complete bipartite graph Km,n and prove the conjecture when m = 5, for arbitrary n ≥ m and r ≥ 2. [ABSTRACT FROM AUTHOR] |
