Abstract
For any graph [Formula: see text], a nonempty subset [Formula: see text] of [Formula: see text] is called an induced-paired dominating set if every vertex in [Formula: see text] is adjacent to some vertex in [Formula: see text], and the induced subgraph [Formula: see text] contains only independent edges. An induced-paired dominating set of [Formula: see text] with minimum number of vertices is also called a [Formula: see text]-set. We define the [Formula: see text]-induced paired dominating graph of [Formula: see text], denoted by [Formula: see text], to be the graph whose vertex set consists of all [Formula: see text]-sets, and two [Formula: see text]-sets are adjacent in [Formula: see text] if they are different from each other by only one vertex. In this paper, we exhibit all [Formula: see text]-induced-paired dominating graphs of paths and cycles.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.