**13**Citations

**15**References

# Equistable graphs

**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.

- CitationsCitations13
- ReferencesReferences15

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**ABSTRACT:**A graph is called equistable when there is a non-negative 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 series-parallel graphs that are equistable, generalizing results of Mahadev, Peled and Sun about equistable outer-planar graphs.0Comments 9Citations - [Show abstract] [Hide abstract]
**ABSTRACT:**A graph is called equistable when there is a non-negative 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 non-simplicial vertices have a common simplicial neighbor.0Comments 11Citations - [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 distance-hereditary. This is used to designa polynomial-time recognition algorithm for equistable distancehereditarygraphs.0Comments 9Citations

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