Folding trees gracefully
When a graceful labeling of a bipartite graph assigns the smaller labels to the vertices of one of the stable sets of the graph, the assignment is called an α-labeling. Any graph that admits such a labeling is an α-graph. In this work we extend the concept of vertex amalgamation to generate a new cl...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2020-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1016/j.akcej.2019.10.001 |
| Summary: | When a graceful labeling of a bipartite graph assigns the smaller labels to the vertices of one of the stable sets of the graph, the assignment is called an α-labeling. Any graph that admits such a labeling is an α-graph. In this work we extend the concept of vertex amalgamation to generate a new class of α-graphs obtained by a sequence of k-vertex amalgamations of t copies of an α-tree. This procedure is also applied to any collection of α-trees such that any pair of trees in this collection have stable sets with the same cardinalities. We also use this idea on other types of α-graphs. In addition, we present a family of α-trees of even diameter formed with four caterpillars of the same size. |
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| ISSN: | 0972-8600 2543-3474 |