On the semitotal dominating sets of graphs
Saeid Alikhani, Hassan Zaherifar

TL;DR
This paper investigates the properties and enumeration of semitotal dominating sets in graphs, including calculations of their minimum size and counts in specific and arbitrary graphs.
Contribution
It introduces the concept of semitotal domination number, computes it for specific graphs, and counts the number of such sets of arbitrary size in some graphs.
Findings
Computed semitotal domination number for specific graphs
Counted the number of semitotal dominating sets of arbitrary size in some graphs
Provided new insights into the structure of semitotal dominating sets
Abstract
A set of vertices in an isolate-free graph is a semitotal dominating set of if is a dominating set of and every vertex in is within distance from another vertex of .The semitotal domination number of is the minimum cardinality of a semitotal dominating set of and is denoted by . In this paper after computation of semitotal domination number of specific graphs, we count the number of this kind of dominating sets of arbitrary size in some graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Graph theory and applications
