Total outer-connected domination number of middle graphs
Farshad Kazemnejad, Behnaz Pahlavsay, Elisa Palezzato, Michele, Torielli
TL;DR
This paper investigates the total outer-connected domination number of middle graphs, providing bounds, exact values for specific graph families, and Nordhaus-Gaddum-like relations, advancing understanding of domination parameters in graph theory.
Contribution
It introduces new bounds and exact computations for the total outer-connected domination number of middle graphs, along with Nordhaus-Gaddum-like relations, enriching the theoretical framework.
Findings
Derived tight bounds in terms of graph order
Computed exact values for specific graph families
Established Nordhaus-Gaddum-like relations
Abstract
In this paper, we study the total outer-connected domination number of the middle graph of a simple graph and we obtain tight bounds for this number in terms of the order of the middle graph. We also compute the total outer-connected domination number of some families of graphs, explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the total outer-connected domination number of middle graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Graph theory and applications