Star and Semi-Star Transformations in Fullerene Graphs

TL;DR

This paper introduces two transformations for fullerene graphs with perfect star packings of type P0, analyzing how these transformations affect the graph's structure and properties.

Contribution

The paper presents new transformations for fullerene graphs with perfect star packings of type P0, expanding understanding of their structural modifications.

Findings

Transformations preserve perfect star packing of type P0.

Characterization of resulting fullerene graphs after transformations.

Insights into structural properties of transformed fullerene graphs.

Abstract

A perfect star packing in a graph G is a spanning subgraph of G whose every component is isomorphic to the star graph $K_{1,3}$. A perfect star packing of a fullerene graph G is of type P0 if all the centers of stars lie on hexagons of G. Many fullerene graphs arise from smaller fullerene graphs by applying some transformations. In this paper, we introduce two transformations for fullerene graphs that have perfect star packing of type P0 and examine some characteristics of the graphs obtained from this transformation.