IJPAM: Volume 15, No. 1 (2004)


Jirimutu$^1$, Bao Yu-Lan$^2$, Kong Fan-Li$^3$
$^{1,2,3}$College of Mathematics and Computer Science
Inner Mongolia University for Nationalities
Tongliao, 028043, P.R. CHINA
$^1$e-mail: jrmt@sina.com
$^2$e-mail: nashun168@sina.com

Abstract.In this paper we discuss the $k-$ gracefulness of $r-$ crown $ I_r(k_{m, n}) $ $ (m \leq n, r \geq 2) $ for complete bipartite graph and prove the conjecture when $ m=2, 3 $, which is advanced by [#!1!#], all crown of complete bipartite graph $ k_{m, n} $ $ (m \leq n) $ are $k-$ graceful graph $ (k \geq 2) $, but it is very difficult to certain when $ m \geq 4 $.

Received: June 6, 2004

AMS Subject Classification: 05C78, 05C50

Key Words and Phrases: complete bipartite graph, graceful graph, $ k$-graceful graph

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 15
Issue: 1