On Center, Periphery and Average Eccentricity for the Convex Polytopes

A vertex v is a peripheral vertex in G if its eccentricity is equal to its diameter, and periphery P ( G ) is a subgraph of G induced by its peripheral vertices. Further, a vertex v in G is a central vertex if e ( v ) = r a d ( G ) , and the subgraph of G induced by its central vertices is called ce...

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Veröffentlicht in:Symmetry (Basel) 2016, Vol.8 (12), p.145-145
Hauptverfasser: Nazeer, Waqas, Kang, Shin Min, Nazeer, Saima, Munir, Mobeen, Kousar, Imrana, Sehar, Ammara, Kwun, Young Chel
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Sprache:eng
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Zusammenfassung:A vertex v is a peripheral vertex in G if its eccentricity is equal to its diameter, and periphery P ( G ) is a subgraph of G induced by its peripheral vertices. Further, a vertex v in G is a central vertex if e ( v ) = r a d ( G ) , and the subgraph of G induced by its central vertices is called center C ( G ) of G . Average eccentricity is the sum of eccentricities of all of the vertices in a graph divided by the total number of vertices, i.e., a v e c ( G ) = { 1 n ∑ e G ( u ) ; u ∈ V ( G ) } . If every vertex in G is central vertex, then C ( G ) = G , and hence, G is self-centered. In this report, we find the center, periphery and average eccentricity for the convex polytopes.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym8120145