Open Access

## A. M. Ismayil and R. Tejaskumar

#### Full Text

In this paper, the concept of eccentric domination polynomial $ED(G,k)= \sum \limits_{k=\gamma_{ed}(G)}^{V(G)} ed(G,k) x^k$ is introduced. Here $\gamma_{ed}(G)$ is the eccentric domination number of a graph $G$ and $ed(G,k)$ is the number of eccentric dominating sets of $G$ of size $k$. Theorems related to eccentric domination polynomials are stated and proved. The eccentric domination polynomials of some standard graphs are computed.

Keywords:
Eccentric dominating set, Eccentric domination number, Eccentric domination polynomial.