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Constructing uniform central graphs and embedding into them

Author

Listed:
  • Sandi Klavžar

    (University of Ljubljana
    University of Maribor
    Institute of Mathematics, Physics and Mechanics)

  • Kishori P. Narayankar

    (Mangalore University, Mangalagangothri)

  • S. B. Lokesh

    (Mangalore University, Mangalagangothri)

Abstract

A graph is called uniform central (UC) if all its central vertices have the same set of eccentric vertices. It is proved that if G is a UC graph with radius at least 3, then substituting a central vertex u of G with an arbitrary graph H and connecting the vertices of H to all neighbors of u (in G), yields a UC graph again. This construction extends several earlier ones and enables a simple argument for the fact that for any r ≥ 2 and any r + 1 ≤ d ≤ 2r, there exists a non-trivial UC graph G with rad(G) = r and diam(G) = d. Embeddings of graphs into UC graphs are also considered. It is shown that if G is an arbitrary graph with at least one edge then at most three additional vertices suffice to embed G into an r-UC graph with r ≥ 2. It is also proved that P3 is the only UC graph among almost self-centered graphs.

Suggested Citation

  • Sandi Klavžar & Kishori P. Narayankar & S. B. Lokesh, 2019. "Constructing uniform central graphs and embedding into them," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(2), pages 451-460, June.
    • Handle: RePEc:spr:indpam:v:50:y:2019:i:2:d:10.1007_s13226-019-0337-4
    DOI: 10.1007/s13226-019-0337-4
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    References listed on IDEAS

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    1. Du, Zhibin, 2017. "Further results regarding the sum of domination number and average eccentricity," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 299-309.
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