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Power domination in certain chemical structures
Stephen, Sudeep Rajan, Bharati Ryan, Joe Grigorious, Cyriac William, Albert
Stephen, Sudeep
Rajan, Bharati
Ryan, Joe
Grigorious, Cyriac
William, Albert
Abstract
Let G(V , E) be a simple connected graph. A set S ⊆ V is a power dominating set (PDS) of G, if every vertex and every edge in the system is observed following the observation rules of power system monitoring. The minimum cardinality of a PDS of a graph G is the power domination number ϓp (G). In this paper, we establish a fundamental result that would provide a lower bound for the power domination number of a graph. Further, we solve the power domination problem in polyphenylene dendrimers, Rhenium Trioxide (ReO3) lattices and silicate networks.
Keywords
Power domination, Polyphenylene dendrimers, ReO 3 lattices, Silicate networks
Date
2015
Type
Journal article
Journal
Book
Volume
33
Issue
Page Range
10-18
Article Number
ACU Department
School of Arts and Humanities
Faculty of Education and Arts
Faculty of Education and Arts
Collections
Relation URI
Event URL
Open Access Status
License
All rights reserved
File Access
Controlled
Notes
©2014 Elsevier B.V. All rights reserved.