Trees with Large Neighborhood Total Domination Number
Michael A. Henning, Kirsti Wash

TL;DR
This paper characterizes extremal trees with maximum neighborhood total domination number, specifically those achieving the upper bound of half the order, and extends the characterization to certain connected graphs.
Contribution
It provides a complete characterization of extremal trees for even order and relates these to connected graphs achieving the maximum neighborhood total domination number.
Findings
Characterization of extremal trees with maximum neighborhood total domination number for even n.
Extension of tree characterization to certain connected graphs.
Identification of specific graph classes achieving the upper bound.
Abstract
In this paper, we continue the study of neighborhood total domination in graphs first studied by Arumugam and Sivagnanam [Opuscula Math. 31 (2011), 519--531]. A neighborhood total dominating set, abbreviated NTD-set, in a graph is a dominating set in with the property that the subgraph induced by the open neighborhood of the set has no isolated vertex. The neighborhood total domination number, denoted by , is the minimum cardinality of a NTD-set of . Every total dominating set is a NTD-set, implying that , where and denote the domination and total domination numbers of , respectively. Arumugam and Sivagnanam posed the problem of characterizing the connected graphs of order achieving the largest possible neighborhood total domination number, namely . A partial…
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Interconnection Networks and Systems
