S-distance in trees

  • Garry L. Johns
  • Tai-Chi Lee
Track1: Graph Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 507)


For a connected graph G, a subset S of V(G) and vertices u, v of G, the S-distance ds(u,v) from u to v is the length of a shortest u — v walk in G that contains every vertex of S. The S-eccentricity es(v) of a vertex v is the maximum S-distance from v to each vertex of G and the S-diameter diamsG is the maximum S-eccentricity among the vertices of G. For a tree T, a formula is given for ds(u,v) and for S ≠ ϕ, it is shown that diamsT is even. Finally, the complexity of finding ds(u,v) is discussed.


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  1. 1.
    G. Chartrand and L. Lesniak, Graphs and Digraphs, 2nd Edition. Wadsworth and Brooks/Cole, Monterey, CA (1986).Google Scholar
  2. 2.
    J. Dossey, A. Otto, L. Spence, C. VanderEynder, Discrete Mathematics. Scott, Foresman and Co., Glenview, IL (1987).Google Scholar
  3. 3.
    G. Johns, S-distance in graphs. Submitted for publication.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Garry L. Johns
    • 1
  • Tai-Chi Lee
    • 2
  1. 1.Department of Mathematical SciencesSaginaw Valley State UniversityUSA
  2. 2.Department of Computer ScienceSaginaw Valley State UniversityUSA

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