Counting perfect edge dominating sets: extremal results and linear-time algorithms
Combinatorics
2026-07-04 v1
Abstract
An edge of a graph \emph{dominates} itself and each edge adjacent to it. A \emph{perfect edge dominating set} is a subset of edges such that each edge outside the subset is dominated by exactly one edge of the subset. In this article, we characterize the extremal graphs on vertices in the classes of trees, forests, and chordal graphs with respect to the number of perfect edge dominating sets. Moreover, we derive linear-time algorithms for counting perfect edge dominating sets and for counting dominating induced matchings in generalized series-parallel graphs and chordal graphs.
Cite
@article{arxiv.2607.03894,
title = {Counting perfect edge dominating sets: extremal results and linear-time algorithms},
author = {Luciano N. Grippo and Min Chih Lin and Verónica Moyano and Camilo Vera},
journal= {arXiv preprint arXiv:2607.03894},
year = {2026}
}