Abstract
For a graph G, with v as any vertex, the maximum distance of v to another vertex or node is defined as the eccentricity \(e\left( v \right)\) of the vertex v. Of all the eccentricities, the minimum is the radius, maximum of the eccentricities is the diameter, of graph G. If the eccentricity of any vertex is equal to the radius, then the vertex is said to be the central vertex of G. So, if for G, every vertex is the center, then G is defined as a graph that is self-centered. Here, we construct and characterize the power graph of any self-centered graph having a regular eccentric sequence. Also, the embedding of special graphs is discussed here.
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