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 graphs. In this paper, we have examined the existence of a few self-graphoidal graphs from path length sequence of a graphoidal cover and obtained new results on self-graphoidal graphs.

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Das P.K. On a graph isomorphic to its intersection graph: self-graphoidal graphs / P.K. Das, K. R. Singh // Algebra and Discrete Mathematics. - 2018. - Vol. 26. - Number 2. - Рp. 247-255

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 ...

A metric basis S of a graph G is the subset
of vertices of minimum cardinality such that all other vertices are
uniquely determined by their distances to the vertices in S. The
metric dimension of a graph G is the ...

Protasova, K. D.(ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)

A finite connected graph G is called square-Hamiltonian if G2 is Hamiltonian. We prove that any join of the family of Hamiltonian graphs by tree is square-Hamiltonian.
Applying this statement we show that the line graph ...