On the Pendant Number of Certain Graphs
P. G. R. S. Ranasinghe *
Department of Mathematics, Faculty of Science, University of Peradeniya, Peradeniya, Sri Lanka.
L. R. M. K. R. Jayathilaka
Department of Mathematics, Faculty of Science, University of Peradeniya, Peradeniya, Sri Lanka.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Complement, decomposition, line graph, pendant number, total graph