Accession Number : ADA262424


Title :   A Class of Planar Well-covered Graphs With Girth Four


Corporate Author : VANDERBILT UNIV NASHVILLE TN DEPT OF MATHEMATICS


Personal Author(s) : Pinter, Michael R


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a262424.pdf


Report Date : Jan 1991


Pagination or Media Count : 26


Abstract : A well-covered graph is a graph in which every maximal independent set is a maximum independent set; Plummer introduced the concept in a 1970 paper. The notion of a 1 -well- covered graph was introduced by Staples in her 1975 dissertation: a well-covered -graph G is 1 -well-covered if and only if G-v is also well-covered for every point v in G. Except for K.) and C5, every 1- well-covered graph contains triangles or 4-cycles. Thus, triangle-free 1 -well- covered graphs necessarily have girth 4. We show that all planar 1-well-covered graphs of girth 4 belong to a specific infinite family, and we give a characterization of this family.


Descriptors :   *GRAPHS , THESES , CYCLES


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE