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Some Transfinite Graph Theory

  • Armen H. Zemanian

Abstract

A peculiarity of transfinite graphs not encountered in conventional graphs is that connectedness by means of paths need not be transitive as a binary relationship between branches. In Section 3.1, we establish a criterion (Condition 3.1-2) under which transfinite connectedness through paths is transitive. The proof of this is far simpler in the present context of pristine graphs than it is for general transfinite graphs [34, Chapter 3]. Moreover, the present criterion combines the two separate ones given in [34, Conditions 3.2-1 and 3.5-1].

Keywords

Terminal Node Finite Subset Maximal Class Pristine Graph Nest Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Armen H. Zemanian
    • 1
  1. 1.Electrical Engineering DepartmentUniversity at Stony BrookStony BrookUSA

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