Level Polynomials of Rooted Trees

Bünyamin Şahin

doi:10.20944/preprints202312.0902.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 12 December 2023 / Approved: 12 December 2023 / Online: 12 December 2023 (16:11:44 CET)

Level index was introduced in 2017 for rooted trees which is a component of Gini index. In the origin, Gini index is a tool for economical investigations but Balaji and Mahmoud defined the graph theoretical applications of this index for statistical analysis of graphs. Level index is an important component of Gini index. In this paper we define a new graph polynomial which is called level polynomial and calculate the level polynomial of some classes of trees. We obtain some interesting relations between the level polynomials and some integer sequences.

Level index; Level polynomial; Triangular Numbers; Subdivision of Stars; Dendrimers

Computer Science and Mathematics, Computer Networks and Communications

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Level Polynomials of Rooted Trees

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