Graceful Labeling of Chain Graphs with Pendants
| Autor: | Indunil, W. K. M., A. A. I. Perera |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| DOI: | 10.5281/zenodo.7439823 |
| Popis: | Graph labeling is one of the most popular research areas in graph theory. There is a vast amount of literature available on graph labeling. In this research, we especially concentrate on a special type of graph labeling method called vertex graceful labeling. A simple connected graph 𝐺 is said to be a vertex graceful if there exists a vertex graceful labeling on the vertices of 𝐺 starting from 1. Graceful labeling of 𝐺 is a vertex labeling which is defined as an injective mapping from to such that the edge labeling defined by is also injective. There is a very famous open conjecture in this area abbreviated as GTC which stands for graceful tree conjecture or Ringel - Kotzig conjecture which hypothesizes that all trees are graceful. In this research work, we introduce graceful labeling for a chain of the key graph with a finite number of pendants and a chain of linear dice graphs with a finite number of pendants. {"references":["Abdul Kader, M., Manjur, S., & Manzur Ankon, Md. T. (2014). A Critical Assessment of Graceful Graphs and Trees: Study and Development of New Approaches. http://dspace.mist.ac.bd:8080/xmlui/handle/123456789/151","Graceful labeling - Wikipedia. (n.d.). Retrieved September 1, 2022, from https://en.wikipedia.org/wiki/Graceful_labeling","Rosa, A. (1967) On Certain Valuations of the Vertices of a Graph. Theory of Graphs (International Symposium, Rome, July 1966), Dunod Gordon & Breach Science Publishers, Inc., New York and Dunod Paris, 349-355. - References - Scientific Research Publishing. (n.d.). Retrieved September 1, 2022, from https://www.scirp.org/(S(czeh2tfqw2orz553k1w0r45))/reference/referencespapers.aspx?referenceid=2964508"]} |
| Databáze: | OpenAIRE |
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