Independent Domination Stable Trees and Unicyclic Graphs

Pu Wu, Huiqin Jiang, Sakineh Nazari-Moghaddam, Seyed Mahmoud Sheikholeslami, Zehui Shao and Lutz Volkmann
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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

Mathematics, 2019, vol. 7, issue 9, 1-17

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.

Keywords: independent domination; stable graph; tree; unicyclic graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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