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arXiv · 2206.15439

Connected and outer-connected domination number of middle graphs

Farshad Kazemnejad·Behnaz Pahlavsay·Elisa Palezzato·Michele Torielli
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Abstract

In this paper, we study the notions of connected domination number and of outer-connected domination number for middle graphs. Indeed, we obtain tight bounds for this number in terms of the order of the graph M(G). We also compute the outer-connected domination number of some families of graphs such as star graphs, cycle graphs, wheel graphs, complete graphs, complete bipartite graphs and some operation on graphs, explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the outer-connected domination number of middle graphs.

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Farshad Kazemnejad, Behnaz Pahlavsay, Elisa Palezzato, Michele Torielli. 2022-06-20. Connected and outer-connected domination number of middle graphs. https://arxiv.org/abs/2206.15439

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