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Np-completeness and bounds for disjunctive total domination subdivision

Author

Listed:
  • Canan Çiftçi

    (Ordu University)

  • Aysun Aytaç

    (Ege University)

Abstract

A subset $$ S\subseteq V(G) $$ S ⊆ V ( G ) , where V(G) is the vertex set of a graph G, is a disjunctive total dominating set of G if each vertex has a neighbour in S or has at least two vertices in S at distance two from it. The minimum cardinality of such a set is the disjunctive total domination number. There are some graph modifications on the edge or vertex of a graph, one of which is subdividing an edge. The disjunctive total domination subdivision number of G is the minimum number of edges which must be subdivided (each edge in G can be subdivided exactly once) to increase the disjunctive total domination number. Firstly, we prove that the disjunctive total domination subdivision problem is NP-complete in bipartite graphs. We next establish some bounds on disjunctive total domination subdivision.

Suggested Citation

  • Canan Çiftçi & Aysun Aytaç, 2025. "Np-completeness and bounds for disjunctive total domination subdivision," Journal of Combinatorial Optimization, Springer, vol. 49(1), pages 1-10, January.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:1:d:10.1007_s10878-024-01245-4
    DOI: 10.1007/s10878-024-01245-4
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