Characterization of Trees with Maximum Security
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917407459639296 |
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| author | Alochukwu, Alex S. A. Dossou-Olory, Audace A. V. Osaye, Fadekemi J. Rakotonarivo, Valisoa R. M. Ravichandran, Shashank Selkirk, Sarah J. Wang, Hua Whitlatch, Hays |
| author_facet | Alochukwu, Alex S. A. Dossou-Olory, Audace A. V. Osaye, Fadekemi J. Rakotonarivo, Valisoa R. M. Ravichandran, Shashank Selkirk, Sarah J. Wang, Hua Whitlatch, Hays |
| contents | The rank (also known as protection number or leaf-height) of a vertex in a rooted tree is the minimum distance between the vertex and any of its leaf descendants. We consider the sum of ranks over all vertices (known as the security) in binary trees, and produce a classification of families of binary trees for which the security is maximized. In addition, extremal results relating to maximum rank among all vertices in families of trees is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterization of Trees with Maximum Security Alochukwu, Alex S. A. Dossou-Olory, Audace A. V. Osaye, Fadekemi J. Rakotonarivo, Valisoa R. M. Ravichandran, Shashank Selkirk, Sarah J. Wang, Hua Whitlatch, Hays Combinatorics 05C05, 05D99, 05C75 The rank (also known as protection number or leaf-height) of a vertex in a rooted tree is the minimum distance between the vertex and any of its leaf descendants. We consider the sum of ranks over all vertices (known as the security) in binary trees, and produce a classification of families of binary trees for which the security is maximized. In addition, extremal results relating to maximum rank among all vertices in families of trees is discussed. |
| title | Characterization of Trees with Maximum Security |
| topic | Combinatorics 05C05, 05D99, 05C75 |
| url | https://arxiv.org/abs/2411.19188 |