Planar Strongly Well-Covered Graphs

Abstract

Plummer introduced the concept of a well-covered graph in 1970. A graph is well-covered if every maximal independent set (with respect to set inclusion) in the graph is also a maximum independent set. Various subclasses of well-covered graphs have been studied. We consider the subclass which we call strongly well-covered graphs. A strongly well-covered graph G is a well-covered graph with the additional property that G-e is also well-covered for every edge e in G. By making use of (1) structural characteristics of strongly well-covered graphs and (2) the theory of Euler contributions (for planar graphs), we show that there are only four planar strongly well-covered graphs.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1991
Accession Number
ADA261945

Entities

People

  • Michael R. Pinter

Organizations

  • Vanderbilt University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Availability
  • Contracts
  • Coverings
  • Graph Theory
  • Inclusions
  • Mathematics
  • Symmetry
  • Tennessee
  • Theses
  • Triangles
  • Universities

Readers

  • Calculus or Mathematical Analysis
  • Database Systems and Applications
  • Plasma Physics / Magnetohydrodynamics