For a graph $G$, let $P(G,lambda)$ denote the chromatic polynomial of $G$.Two graphs $G$ and $H$ are chromatically equivalent if they Playground share the same chromatic polynomial.A graph $G$ is chromatically unique if for any graph chromatically equivalent to Link Assembly $G$ is isomorphic to $G$.In this paper, the chromatically unique of a new family of 6-bridge graph $ heta(a,a,a,b,b,c)$ where $2le ale ble c$ is investigated.