Rogers 𝑱 index

Mareike Fischer, Lina Herbst, Sophie Johanna Kersting, Annemarie Luise Kühn and Kristina Wicke
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Mareike Fischer: University of Greifswald, Institute of Mathematics and Computer Science
Lina Herbst: Department of English and American Studies Friedrich Schiller University Jena
Sophie Johanna Kersting: University of Greifswald, Institute of Mathematics and Computer Science
Annemarie Luise Kühn: University of Greifswald, Institute of Mathematics and Computer Science
Kristina Wicke: New Jersey Institute of Technology, Department of Mathematical Sciences

Chapter Chapter 19 in Tree Balance Indices, 2023, pp 225-230 from Springer

Abstract: Abstract The Rogers 𝑱 index (also known as the “number of unbalanced vertices” 𝑈) is an imbalance index for binary trees that was introduced by Rogers [123]. Similar to the Colless index, its idea is based on the concept of a classic scale, which is in a balanced state only if both sides of the lever have the same weight attached to it. However, instead of measuring the degree of imbalance at each inner vertex and summing up these values like the Colless index (Chapter 12), it simply counts the number of inner vertices that have a balance value greater than zero, i.e., that are not perfectly balanced.

Date: 2023
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DOI: 10.1007/978-3-031-39800-1_19

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