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Power domination in tree derived architectures
J. Anitha,
Published in Charles Babbage Research Centre
Volume: 112
Pages: 53 - 63
A set 5 of vertices in a graph G is called a dominating set of G if every vertex in V(G)\S is adjacent to some vertex in 5. A set S is said to be a power dominating set of G if every vertex in the system is monitored by the set S following a set of rules for power system monitoring. A zero forcing set of G is a subset of vertices B such that if the vertices in B are colored blue and the remaining vertices are colored white initially, repeated application of the color change rule can color all vertices of G blue. The power domination number and the zero forcing number of G are the minimum cardinality of a power dominating set and the minimum cardinality of a zero forcing set respectively of G. In this paper, we obtain the power domination number, total power domination number, zero forcing number and total forcing number for m-rooted sibling trees,/-sibling trees and l-binary trees. We also solve power domination number for circular ladder, Mobius ladder, and extended cycle-of-ladder. © 2020 Charles Babbage Research Centre. All rights reserved.
About the journal
JournalJournal of Combinatorial Mathematics and Combinatorial Computing
PublisherCharles Babbage Research Centre