Open Access

## A. M. Ismayil and S. Muthupandiyan

#### Full Text

A g-eccentric dominating set $D\subseteq V$ of a fuzzy graph $G=(\rho,\phi)$ is said to be a complementary nil g-eccentric dominating set (CNGED-set) if $V-D$ contains no g-eccentric dominating set of $G=(\rho,\phi)$. The least scalar cardinality taken over all CNGED-set of $G$ is called the complementary nil g-eccentric domination number of $G=(\rho,\phi)$. In this article, bounds for complementary nil g-eccentric domination number for a few standard fuzzy graph are given and theorems related to CNGED-sets are discussed. The relation between complementary nil g-eccentric domination number and other well-known parameters are analyzed.

Keywords:
Enclave, Complementary nil domination number, Complementary nil g-eccentric domination number.