Algorithmic Aspects of Outer-Independent Double Roman Domination in Graphs

Abstract

Let [Formula: see text] be graph. For any function [Formula: see text], let [Formula: see text], [Formula: see text]. The function [Formula: see text] is called an outer-independent double Roman dominating function (OIDRDF) if the following conditions are satisfied. (i) If [Formula: see text], then [Formula: see text] or [Formula: see text] (ii) If [Formula: see text], then [Formula: see text] (iii) [Formula: see text] is independent. The outer-independent double Roman domination number of [Formula: see text] is defined by [Formula: see text] is an OIDRDF OF [Formula: see text]. We prove that the decision problem MOIDRDP, corresponding to [Formula: see text] is NP-complete for split graphs. We also show that it is linear time solvable for connected threshold graphs and bounded treewidth graphs. Finally, we show that the MOIDRDP and domination are not equivalent in computational complexity aspects.