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Independent Domination Stable Trees and Unicyclic Graphs

Author

Listed:
  • Pu Wu

    (Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China)

  • Huiqin Jiang

    (Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China)

  • Sakineh Nazari-Moghaddam

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 5375171379, Iran)

  • Seyed Mahmoud Sheikholeslami

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 5375171379, Iran)

  • Zehui Shao

    (Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China)

  • Lutz Volkmann

    (Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen, Germany)

Abstract

A set S ⊆ V ( G ) in a graph G is a dominating set if S dominates all vertices in G , where we say a vertex dominates each vertex in its closed neighbourhood. A set is independent if it is pairwise non-adjacent. The minimum cardinality of an independent dominating set on a graph G is called the independent domination number i ( G ) . A graph G is ID-stable if the independent domination number of G is not changed when any vertex is removed. In this paper, we study basic properties of ID-stable graphs and we characterize all ID-stable trees and unicyclic graphs. In addition, we establish bounds on the order of ID-stable trees.

Suggested Citation

  • Pu Wu & Huiqin Jiang & Sakineh Nazari-Moghaddam & Seyed Mahmoud Sheikholeslami & Zehui Shao & Lutz Volkmann, 2019. "Independent Domination Stable Trees and Unicyclic Graphs," Mathematics, MDPI, vol. 7(9), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:820-:d:264553
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