More results on weighted independent domination

TL;DR

This paper investigates the computational complexity of weighted independent domination, proving NP-hardness in certain graph classes while identifying new classes where the problem can be solved efficiently.

Contribution

It extends NP-hardness results to a subclass of sat-graphs and chordal graphs and introduces two new graph classes with polynomial-time solutions.

Findings

NP-hard in a subclass of sat-graphs and chordal graphs

Polynomial-time solutions in two new graph classes

Strengthens understanding of problem complexity in restricted graph classes

Abstract

Weighted independent domination is an NP-hard graph problem, which remains computationally intractable in many restricted graph classes. In particular, the problem is NP-hard in the classes of sat-graphs and chordal graphs. We strengthen these results by showing that the problem is NP-hard in a proper subclass of the intersection of sat-graphs and chordal graphs. On the other hand, we identify two new classes of graphs where the problem admits polynomial-time solutions.