Proofs For Progressively Generalized Fibonacci Identities Using Maximal Independent Sets of Tree Graphs

TL;DR

This paper extends a graph-theoretic proof method to derive a broad class of Fibonacci identities, analyzing their properties and generalizations to an infinite extent.

Contribution

It introduces a generalized proof technique for Fibonacci identities based on maximal independent sets of tree graphs, expanding previous methods.

Findings

Generalized Fibonacci identities derived using graph theory

Characterization of properties of these identities

Infinite generalizations explored

Abstract

This paper generalizes a graph theoretic proof technique for a Fibonacci identity proposed by Lee Knisley Sanders, and explores characteristics of these generalized theorems ad infinitum.