Total domination number of middle graphs
Farshad Kazemnejad, Behnaz Pahlavsay, Elisa Palezzato, Michele, Torielli
TL;DR
This paper investigates the total domination number of middle graphs, providing bounds, explicit calculations for certain graph families, and Nordhaus-Gaddum-like relations, advancing understanding of domination properties in this graph class.
Contribution
It introduces bounds and exact values for the total domination number of middle graphs, and explores related inequalities, filling gaps in the graph domination literature.
Findings
Tight bounds for total domination number in terms of graph order.
Explicit calculations for specific graph families.
Nordhaus-Gaddum-like relations for middle graphs.
Abstract
A total dominating set of a graph G with no isolated vertices is a subset S of the vertex set such that every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set of G. In this paper, we study the total domination number of middle graphs. Indeed, we obtain tight bounds for this number in terms of the order of the graph G. We also compute the total domination number of the middle graph of some known families of graphs explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the total domination number of middle graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Interconnection Networks and Systems