Non-negative unique isolated signed dominating function of graphs

  • Duraisamy Kumar SRM TRP Engineering College,\\ Tiruchirapalli-621105, Tamil Nadu, India.
  • P. Thangaraj KPR Institute of Engineering and Technology,\\ Coimbatore-641407, Tamil Nadu, India.
  • N. Jayalakshmi Research Scholar, Bharathiar University,\\ Coimbatore-641046, \ Tamil Nadu,\ India.


A function $\lambda:V(G)\rightarrow \{-1,+1 \}$ is said to be a non-negative unique isolated signed dominating function(NNUISDF) of a graph $G$ if $\sum\limits_{u \in N[v]} \lambda(u) \geq 0$ for all $v \in V(G)$ and for excatly one vertex of $w \in V(G)$, $\lambda(N[w])= 0$. A Non-negative unique isolated signed domination number(NNUISDN) of $G$, denoted by $\gamma^{NNU}_{is}(G)$, is the minimum weight of a NNUISDF of $G$. In this article, we study some of the basic properties of NNUISDF and we give NNUISDN for disconnected graphs, paths and some families of graphs.