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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Farshad Kazemnejad
Faculty of Basic Sciences, Department of Mathematics, Ilam University, Iran
Electrical & Electronics Engineering

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Total domination number of middle graphs Farshad Kazemnejad; Behnaz Pahlavsay; Elisa Palezzato; Michele Torielli
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2022.10.1.19

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. 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. 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.
Co-Authors Behnaz Pahlavsay Elisa Palezzato Michele Torielli