Graphs of separability at most k are defined as graphs in which every two non-adjacent vertices are separated by a set of at most k other vertices. For k ∈ {0,1}, the only connected graphs of separability at most k are complete graphs and block graphs, respectively. For k ≥ 3, graphs of separability at most k form a rich class of graphs containing all graphs of maximum degree k. Graphs of separability at most 2 generalize complete graphs, cycles and trees. We prove several characterizations of graphs of separability at most 2 and examine some of their consequences.

Graphs of Separability at Most Two: Structural Characterizations and Their Consequences

Cicalese, Ferdinando;
2011-01-01

Abstract

Graphs of separability at most k are defined as graphs in which every two non-adjacent vertices are separated by a set of at most k other vertices. For k ∈ {0,1}, the only connected graphs of separability at most k are complete graphs and block graphs, respectively. For k ≥ 3, graphs of separability at most k form a rich class of graphs containing all graphs of maximum degree k. Graphs of separability at most 2 generalize complete graphs, cycles and trees. We prove several characterizations of graphs of separability at most 2 and examine some of their consequences.
2011
9783642169571
AS graph, Block graphs, Complete graphs, Connected graph, Maximum degree, Nonadjacent vertices, Structural characterization
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/931698
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