On the Pendant Number of Certain Graphs

The present study investigates the pendant number of certain graph classes; complement, line graphs, and total graphs. The pendant number is the minimum number of end vertices of paths in a path decomposition of a graph. A path decomposition of a graph is a decomposition of it into subgraphs; i.e., a sequence of a subset of vertices of the graph such that the endpoints of each edge appear in one of the subsets and each vertex appears in an adjacent sub-sequence of the subsets.