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Neighborhood degree lists of graphs |
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| Authors: | Michael D. Barrus Elizabeth A. Donovan |
| Affiliation: | 1. Department of Mathematics, University of Rhode Island, Kingston, RI 02881, United States;2. Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, United States |
| Abstract: | The neighborhood degree list (NDL) is a graph invariant that refines information given by the degree sequence and joint degree matrix of a graph and is useful in distinguishing graphs having the same degree sequence. We show that the space of realizations of an NDL is connected via a switching operation. We then determine the NDLs that have a unique realization by a labeled graph; the characterization ties these NDLs and their realizations to the threshold graphs and difference graphs. |
| Keywords: | Degree sequence Threshold graph Difference graph Neighborhood degree list |
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