×

Vertex-graceful graphs. (English) Zbl 1217.05198

Summary: A \((p,q)\)-graph \(G = (V, E)\) is called vertex-graceful if it admits a vertex graceful numbering, which is defined as an injection \(f : E \rightarrow \{{0, 1, 2,\ldots, q^{\ast}}\}\), \(q^{\ast} =\) max\(\{p,q\}\) such that the function \(f^{V}: V \rightarrow \mathbb N\) defined by the rule \(f^{V}(v)=\) max \(\{f(e) : e \in E_{v}\) and \(v \in e \} \).
\(\min \{ f(e) : e \in E_{v}\) and \(v \in e \}\) satisfies the property that \(f^{V}(V) := \{ f^{V}(u) : u \in V\} = \{ 1,2,\ldots,p\}\) , where \(E_{v}\) denotes the set of edges in \(G\) that are incident at \(v\) and \(\mathbb N\) denotes the set of natural numbers. A study of this new notion is the prime objective of this paper.

MSC:

05C78 Graph labelling (graceful graphs, bandwidth, etc.)
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Acharya B. D., Research Report 1, in: Graceful hypergraphs
[2] Berge C., Graphs and Hypergraphs (1973)
[3] Golomb S. W., Graph Theory and Computing pp 23– (1972) · doi:10.1016/B978-1-4832-3187-7.50008-8
[4] Harary F., Graph Theory (1969)
[5] Parthasarathy K. R., Basic Graph Theory (1994)
[6] Rosa A., Theorie des Graphes pp 349– (1968)
[7] West D. B., Introduction to Graph Theory (1996) · Zbl 0845.05001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.