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- W990018332 abstract "The periphery of a graph G is the subgraph of G induced by the vertices in G whose eccentricity equals the diameter of G. Graphs that are peripheries of graphs with specified diameter are characterized. For a graph G, the antipodal graph A(G) of G is the graph having the same vertex set as G and edge set E(A(G)) = {uv ∣ u, v ∈ V(G) and dG(u, v) = diam G}. For a graph G and positive integer n, the nth iterated antipodal graph An(G) of G is defined as the graph A(An−1(G)) where Al(G) is A(G) and A0(G) denotes G. It is shown that there exist nonnegative integers n1 and n2 such that n1 < n2 and $$ {{A}^{{{{n}_{1}}}}}(G) cong {{A}^{{{{n}_{2}}}}}(G) $$ . The smallest postitive integer k for which there exists an integer ℓ such that Aℓ(G) ≅ Aℓ+k(G) is called the antipodal period of G. It is shown that for every positive integer k there exists a graph with antipodal period k." @default.
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- W990018332 date "1990-01-01" @default.
- W990018332 modified "2023-10-16" @default.
- W990018332 title "On Peripheral Vertices in Graphs" @default.
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- W990018332 doi "https://doi.org/10.1007/978-3-642-46908-4_22" @default.
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