Unique isolate dom-chromatic number in graphs

  • Sivagnanam Mutharasu Department of Mathematics, CBM College, \\ Coimbatore -641 042,\ Tamil Nadu,\ India.
  • K. Muralidharan Department of Science and Humanities, Dhaanish Ahmed Institute of Technology, \\ Coimbatore -641 105,\ Tamil Nadu,\ India.
  • C. Vanitha Department of Mathematics, Sri Shakthi Institute of Engineering and Technology,\\ Coimbatore-62,Tamil Nadu,\ India.


An unique isolate dom-coloring set(UIDC-set) $D$ of a graph $G$ is a Dom-coloring set(DC-set) $D\subseteq V(G)$ such that $\langle D\rangle$ has exactly one isolated vertex. The minimum cardinality of a minimal UIDC-set is called unique isolate dom-chromatic number(UIDC-number) of $G$, it is denoted by $\gamma_{0,dc}^U(G)$. In this paper, we introduce and study some properties of UIDC-set and we give UIDC-number of some families of graphs.