Abstract
Let G = (V(G),E(G)) be a simple connected graph. A set S ⊆ V(G) is a weakly connected hop dominating set of G if for every q ∈ V \ S, there exists r ∈ S such that dG(q,r) = 2, the subgraph weakly induced by S, denoted by ⟨S⟩w = ⟨NG[S],Ew⟩ where Ew = {qr ∈ E(G) : q ∈ S or r∈S } is connected and S is a dominating set of G. The minimum cardinality of a weakly connected hop dominating set of G is called weakly connected hop domination number and is denoted by γwh(G). In this paper, the authors show and explore the concept of weakly connected hop dominating set. The weakly connected hop dominating set of some special graphs, shadow of graphs, join, corona and Lexicographic product of two graphs are characterized. Also, the weakly connected domination number of the aforementioned graphs are determined. Keywords: weakly connected set, hop dominating set, hop domination number, weakly connected hop dominating set, and weakly connected hop domination number
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 callDisclaimer: 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.
