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Eccentricity Sum in Trees
Discrete Applied Mathematics
  • Heather Smith, University of South Carolina
  • Laszlo A. Szekely, University of South Carolina
  • Hua Wang, Georgia Southern University
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The eccentricity of a vertex, eccT(v)=maxu∈TdT(v,u), was one of the first, distance-based, tree invariants studied. The total eccentricity of a tree, Ecc(T), is the sum of eccentricities of its vertices. We determine extremal values and characterize extremal tree structures for the ratios Ecc(T)/eccT(u), Ecc(T)/eccT(v), eccT(u)/eccT(v), and eccT(u)/eccT(w) where u,w are leaves of T and v is in the center of T. In addition, we determine the tree structures that minimize and maximize total eccentricity among trees with a given degree sequence.


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Citation Information
Heather Smith, Laszlo A. Szekely and Hua Wang. "Eccentricity Sum in Trees" Discrete Applied Mathematics Vol. 207 (2016) p. 120 - 131 ISSN: 0166-218X
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