The Median of Sierpinski Triangle Graphs

TL;DR

This paper determines the median vertices of Sierpiński triangle graphs, which are formed by contracting edges in recursive fractal structures, providing insights into their centrality properties.

Contribution

It explicitly characterizes the median set of Sierpiński triangle graphs, a novel analysis of their centrality in fractal graph structures.

Findings

Median vertices identified for Sierpiński triangle graphs.

Provides formulas or methods for median calculation.

Enhances understanding of graph centrality in fractal graphs.

Abstract

The median $M$ of a graph $G$ is the set of vertices with a minimum total distance to all other vertices in the graph. In this paper, we determine the median of Sierpi\'{n}ski triangle graphs. Sierpi\'{n}ski triangle graphs, also known as Sierpi\'{n}ski gasket graphs of order $n$ are graphs formed by contracting all non-clique edges from the Sierpi\'{n}ski graphs of order ($n+1$).