On the semitotal dominating sets of graphs

2021/07/03 by ‎Saeid Alikhani, Alikhani, Saeid, Hassan Zaherifar +1
Computer Science · Mathematics · #05C15 #05C25 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2107.01424

openalex publication_date 2021/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A set D of vertices in an isolate-free graph G is a semitotal dominating set of G if D is a dominating set of G and every vertex in D is within distance 2 from another vertex of D.The semitotal domination number of G is the minimum cardinality of a semitotal dominating set of G and is denoted by γ_t2(G). 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.

Citations

• On the number of outer connected dominating sets of graphs

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