An Atlas of Different Distances Sets Polynomials of Graphs of Order at most Six

Abstract

The different distances sets polynomial of a graph $G$ of order $p$ is defined as $D_{d}(G,x)=\sum\limits_{i=1}^pd_{d}(G,i)x^i$, where $d_{d}(G,i)$ is the number of different distances sets polynomials of $G$ of size $i$, \cite{Alsinai}. We call the roots of different distances sets polynomial of a graph the different distances roots of that graph. In this article, we compute different distances sets polynomial of all graphs of order less than or equal six and their roots and present them in tables.