Article
Equistable graphs
Journal of Graph Theory (Impact Factor: 0.63). 05/1994; 18(3):281  299. DOI: 10.1002/jgt.3190180307
ABSTRACT
An equistable graph is a graph for which the incidence vectors of the maximal stable sets are the 0–1 solutions of a linear equation. A necessary condition and a sufficient condition for equistability are given. They are used to characterize the equistability of various classes of perfect graphs, outerplanar graphs, and pseudothreshold graphs. Some classes of equistable graphs are shown to be closed under graph substitution.

Article: Equistable series  parallel graphs
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ABSTRACT: A graph is called equistable when there is a nonnegative weight function on its vertices such that a set S of vertices has total weight 1 if and only if S is maximal stable. We characterize those seriesparallel graphs that are equistable, generalizing results of Mahadev, Peled and Sun about equistable outerplanar graphs. 
Article: Equistable chordal graphs
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ABSTRACT: A graph is called equistable when there is a nonnegative weight function on its vertices such that a set S of vertices has total weight 1 if and only if S is maximal stable. We show that a chordal graphs is equistable if and only if every two adjacent nonsimplicial vertices have a common simplicial neighbor.  [Show abstract] [Hide abstract]
ABSTRACT: A graph is called equistable when there is a nonnegativeweight function on its vertices such that a set S of verticeshas total weight 1 if and only if S is maximal stable. We show thata necessary condition for a graph to be equistable is su#cient whenthe graph in question is distancehereditary. This is used to designa polynomialtime recognition algorithm for equistable distancehereditarygraphs.
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