Independence and Domination in Path Graphs of Trees

The problems of determining the maximum cardinality of an independent set of vertices and the minimum cardinality of a maximal independent set of vertices of a graph are known to be NP-complete. We provide efficient algorithms for finding these values for path graphs of trees

Independence Number in Path Graphs

In the paper we present results, which allow us to compute the independence numbers of $P_2$-path graphs and $P_3$-path graphs of special graphs. As $P_2(G)$ and $P_3(G)$ are subgraphs of iterated line graphs $L^2(G)$ and $L^3(G)$, respectively, we compare our results with the independence numbers of corresponding iterated line graphs