Combinatorial Perron parameters for trees
The notion of combinatorial Perron value was introduced in [2]. We continue the study of this parameter and also introduce a new parameter πe(M) which gives a new lower bound on the spectral radius of the bottleneck matrix M of a rooted tree. We prove a bound on the approximation error for πe(M). Se...
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| Other Authors: | , |
| Format: | article |
| Language: | eng |
| Published: |
2020
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10773/25122 |
| Country: | Portugal |
| Oai: | oai:ria.ua.pt:10773/25122 |
| Summary: | The notion of combinatorial Perron value was introduced in [2]. We continue the study of this parameter and also introduce a new parameter πe(M) which gives a new lower bound on the spectral radius of the bottleneck matrix M of a rooted tree. We prove a bound on the approximation error for πe(M). Several properties of these two parameters are shown. These ideas are motivated by the concept of algebraic connectivity. A certain extension property for the combinatorial Perron value is shown and it allows us to define a new center concept for caterpillars. We also compare computationally this new center to the so-called characteristic set, i.e., the center obtained from algebraic connectivity. |
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