# Non-negative unique isolated signed dominating function of graphs

### Abstract

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.

Published

2022-11-24

Section

Articles