The (proper) power graph of a group is a graph whose vertex set is the set of all (nontrivial) elements of the group and two distinct vertices are adjacent if one is a power of the other. Various kinds of planarity of (proper) power graphs of groups are discussed.

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Doostabadi A. Embeddings of (proper) power graphs of finite groups / A. Doostabadi, D.G. Farrokhi // Algebra and Discrete Mathematics. - 2017. - Vol. 24. - Number 2. - Рp. 221-234

Das, P.K.; Singh, K.R.(ДЗ "ЛНУ імені Тараса Шевченка", 2018)

Abstract . A graph G is called a graphoidal graph if there exists a graph H and a graphoidal cover ψ of H such that G ∼= Ω(H, ψ). Then the graph G is said to be self-graphoidal if it is isomorphic to one of its graphoidal ...

Chacko, B.; Dominic, C.; Premodkumar, K. P.(ДЗ "ЛНУ імені Тараса Шевченка", 2019)

In [10], the notion of the splitting graph of a graph
was introduced. In this paper we compute the zero forcing number
of the splitting graph of a graph and also obtain some bounds
besides finding the exact value of ...

Magic rectangles are a classical generalization of
the well-known magic squares, and they are related to graphs. A
graph G is called degree-magic if there exists a labelling of the edges
by integers 1, 2, . . . , |E(G)| ...