Reliability Polynomials of Simple Graphs having Arbitrarily many Inflection Points

TL;DR

This paper demonstrates that for any number n, there exists a simple graph whose reliability polynomial has at least n inflection points, showing the complexity possible in graph reliability functions.

Contribution

It proves the existence of simple graphs with reliability polynomials having arbitrarily many inflection points, expanding understanding of polynomial complexity in graph theory.

Findings

Existence of simple graphs with arbitrarily many inflection points in their reliability polynomials

Reliability polynomials can exhibit complex behavior with multiple inflections

Advances the theoretical understanding of graph reliability functions

Abstract

In this paper we show that for each $n$, there exists a simple graph whose reliability polynomial has at least $n$ inflection points.