Work

Complexity of 2-rainbow total domination problem

Year: 2024

Type: article

Abstract: In this paper,we extend the findings of recent studies on $k$-rainbow total domination by placing our focus on its computational complexity aspects. We show that the problem of determining whether a graph has a $2$-rainbow total dominating function of a given weight is NP-complete. This complexity result holds even when restricted to planar graphs. Along the way tight bounds for the $k$-rainbow total domination number of rooted product graphs are established. In addition, we obtain the closed formula for the $k$-rainbow total domination number of the corona product $G ∗ H$, provided that $H$ has enough vertices.

Source: DiRROS repository (University of Maribor)

Authors: Kraner Šumenjak, Tadeja, Tepeh, Aleksandra

Institutions: University of Maribor, Institute of Mathematics, Physics, and Mechanics

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Javna Agencija za Raziskovalno Dejavnost RS

Awards: Complex networks, Graph theory

OpenAlex ID: W7045963290

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