| Autor: |
Beaton, Iain, Schoonhoven, Sam |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
A polynomial is said to be unimodal if its coefficients are non-decreasing and then non-increasing. The domination polynomial of a graph $G$ is the generating function of the number of dominating sets of each cardinality in $G$. In \cite{IntroDomPoly2014} Alikhani and Peng conjectured that all domination polynomials are unimodal. In this paper we show that not all trees have log-concave domination polynomial. We also give non-increasing and non-decreasing segments of coefficents in trees. This allows us to show the domination polynomial trees with $\Gamma(T)-\gamma(T)<3$ are unimodal. |
| Databáze: |
arXiv |
| Externí odkaz: |
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