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A set \(S\) 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 \(S\). 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, l-sibling trees and I-binary trees. We also solve power domination number for circular ladder, Möbius ladder, and extended cycle-of-ladder.