Golden ratio in graph theory: A survey

TL;DR

This survey explores the intriguing presence and significance of the golden ratio in various aspects of graph theory, including spanning trees, topological indices, and graph coloring.

Contribution

It compiles and reviews existing research on the applications and relevance of the golden ratio in multiple graph theory topics.

Findings

Golden ratio appears in the enumeration of spanning trees.

It influences topological indices and graph energy.

The ratio relates to chromatic and domination roots.

Abstract

Much has been written about the golden ratio $\phi=\frac{1+\sqrt{5}}{2}$ and this strange number appears mysteriously in many mathematical calculations. In this article, we review the appearance of this number in the graph theory. More precisely, we review the relevance of this number in topics such as the number of spanning trees, topological indices, energy, chromatic roots, domination roots and the number of domatic partitions of graphs.