Power domination number of the middle graph

At least 4 years old · documented by

Let GG be any graph, and let M(G)M(G) denote its middle graph. Write γp(M(G))\gamma_p(M(G)) for the power domination number of M(G)M(G) and γ′(G)\gamma^{'}(G) for the edge domination number of GG. Power domination–edge domination conjecture. For any graph GG,

γp(M(G))=γ′(G).\gamma_p(M(G)) = \gamma^{'}(G).

This is presented as an open problem concerning the relationship between power domination in middle graphs and edge domination in the original graph.

References

Primary source

Najibeh Shahbaznejad, Adel P Kazemi and Ignacio M Pelayo, “Some Families of Graphs with Small Power Domination Number”, arXiv:2106.13496 (2021).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.