Total domination number of 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.
Cite
@article{arxiv.2204.07040,
title = {Total domination number of middle graphs},
author = {Farshad Kazemnejad and Behnaz Pahlavsay and Elisa Palezzato and Michele Torielli},
journal= {arXiv preprint arXiv:2204.07040},
year = {2022}
}
Comments
To appear in the Electronic Journal of Graph Theory and Applications. arXiv admin note: substantial text overlap with arXiv:2008.02975