Year: 2024
Type: article
Abstract: A set [Formula: see text] of vertices of a simple graph [Formula: see text] is a strong dominating set, if for every vertex [Formula: see text] there is a vertex [Formula: see text] with [Formula: see text] and [Formula: see text]. The strong domination number [Formula: see text] is defined as the minimum cardinality of a strong dominating set. The strong domatic number [Formula: see text] is the maximum number of strong dominating sets into which the vertex set of [Formula: see text] can be partitioned. We initiate the study of the strong domatic number, and we present different sharp bounds on [Formula: see text]. In addition, we determine this parameter for some classes of graphs such as cubic graphs of order at most [Formula: see text].
Authors: Nima Ghanbari, Saeid Alikhani
Institutions: University of Bergen, Yazd University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404416417