Roman Fractional Bondage Number of a Graph

Abstract

A Roman dominating function on a graph $G$ is a labeling $f:V(G)\to \{0,1,2\}$ such that every vertex with label $0$ has a neighbor with label $2$. The weight of a Roman dominating function is the value $f(V(G))=\sum _{u\in V(G)}f(u)$. The minimum weight of a Roman dominating function on a graph $G$ is called the Roman domination number, denoted by ${\gamma }_R(G)$. The Roman bondage number of a graph $G$ is the cardinality of a smallest set of edges whose removal results in a graph with Roman domination number greater than that of $G$.

In this paper, we initiate the study of the Roman fractional bondage number, and we present different bounds on Roman fractional bondage. In addition, we determine the Roman fractional bondage number of some classes of graphs.