Abstract
The graphoidal graph G of graph H is the graph obtained by taking graphoidal cover Ψ of H as vertices and two vertices are adjacent if and only if the corresponding paths have a non-empty intersection. If G is isomorphic to one of its graphoidal graphs, then G is said to be a self-graphoidal graph. G is called self-complementary graphoidal graph if it is isomorphic to one of its complementary graphoidal graphs. In this article, we characterize self-graphoidal graphs and give a construction of self-graphoidal graphs from cycle and wheel graphs. Also, we give a characterization of self-complementary graphoidal graphs.
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