An Atlas of Roman Domination Polynomials of Graphs of Order at Most Six.

The Roman domination polynomial of a graph G of order p is defined as R(G, x) = ∑2n j=γR(G) r(G, j)x j, where r(G, j) is the number of Roman dominating functions of G of weight j [5]. The roots of a Roman domination polynomial of a graph are called the Roman domination roots of that graph. In this article, the Roman domination polynomials of all the connected graphs of order less than or equal to six are obtained and their roots are computed. Furthermore, all these graphs and their Roman domination polynomials and roots are illustrated in a table. [ABSTRACT FROM AUTHOR]