On probe classes of graphs

Ridder, H. N. de; Lê, Van Bang; Bayer, Daniel

doi:10.1016/j.endm.2006.08.037

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“…Given a class of graphs G , a graph G is a probe graph of G if its vertices can be partitioned into a set P of probes and an independent set N of nonprobes such that G can be extended to a graph of G by adding edges between certain nonprobes. In this way, many more probe graph classes have been defined and widely investigated, eg., probe split graphs, probe chordal graphs, probe tolerance graphs, probe threshold graphs and others [2,6,18,19]. Among all such studies nothing has been said about the nature of adjacency matrices of probe interval graphs until now.…”

Section: Introductionmentioning

confidence: 99%

Characterizations of probe interval graphs

Ghosh,

Podder,

Sen

2008

Preprint

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In this paper we obtain several characterizations of the adjacency matrix of a probe interval graph. In course of this study we describe an easy method of obtaining interval representation of an interval bipartite graph from its adjacency matrix. Finally, we note that if we add a loop at every probe vertex of a probe interval graph, then the Ferrers dimension of the corresponding symmetric bipartite graph is at most 3.

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Section: Introductionmentioning

confidence: 99%