Abstract
Let be an integer and G a simple graph with vertex set V(G). Let f be a function that assigns labels from the set to the vertices of G. For a vertex the active neighbourhood AN(v) of v is the set of all vertices w adjacent to v such that A [k]-Roman dominating function (or [k]-RDF for short) is a function satisfying the condition that for any vertex with f(v) < k, The weight of a [k]-RDF is and the [k]-Roman domination number of G is the minimum weight of an [k]-RDF on G. In this paper we shall be interested in the study of the [k]-Roman domination subdivision number sd of G defined as the minimum number of edges that must be subdivided, each once, in order to increase the [k]-Roman domination number. We first show that the decision problem associated with sd is NP-hard. Then various properties and bounds are established.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: AKCE International Journal of Graphs and Combinatorics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
