Independent Domination Stable Trees and Unicyclic Graphs

Mathematics

卷:7

SeyedMahmoud Sheikholeslami¹  Sakineh Nazari-Moghaddam¹  Pu Wu²  Zehui Shao²  Huiqin Jiang²  Lutz Volkmann³ 

[1] Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 5375171379, Iran;

[2] Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China;

[3] Lehrstuhl II für Mathematik, RWTH Aachen University, 52056 Aachen, Germany;

关键词: independent domination;    stable graph;    tree;    unicyclic graph;   

DOI  :  10.3390/math7090820

来源: DOAJ

【 摘 要 】

A set $S\subseteq V\left(G\right)$ 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 $i\left(G\right)$ . 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.

【 授权许可】

Unknown