IJPAM: Volume 69, No. 3 (2011)

A SURVEY OF THE GRACEFULNESS OF DIGRAPHS

Wei Feng$^1$, Chunlei Xu$^2$, Jirimutu$^3$
$^{1,3}$College of Mathematics
Inner Mongolian University for Nationalities
Tongliao, 028043, P.R. CHINA
$^3$e-mail: [email protected]
$^2$College of Computer Science And Technology
Inner Mongolian University for Nationalities
Tongliao 028043, P.R. CHINA


Abstract. Graph labeling traces its origin to the famous conjecture that all trees are graceful presented by A.Rosa in 1966. In recent years, many research papers on graceful graph have been published. In this survey we have collected studies on the gracefulness of the directed circuit $\vec{C}_m$ and the union graph of mutually non-intersecting $\vec{C}_m$, the digraph  $n\cdot \vec {C}_m$, the digraph $n-\vec{C}_m$, the union of the digraph  $n\cdot \vec {C}_3$, and give some results.

Received: December 1, 2010

AMS Subject Classification: 05C65

Key Words and Phrases: digraph, directed circuit, graceful graph, graceful labeling, conjecture

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 3